A sound basis to Rotational Dynamics

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  • edited February 1

    The general relativity
    Examine carefully the assumptions .
    The space time coordinate system compares 2 reference frames . The fixed coordinate frame is the one which the elevator is moving relative to . The position in the moving reference frame of anything at rest in the fixed frame is given by the expression where the velocity is measured in the fixed reference frame.
    Intuitively we expect a fixed point to have a velocity measured in the moving reference frame. .

    However Galileo placed the person in a moving reference in a sealed box. That observer will not be able to observe any motion.

    Again in the accelerated case the observer will not be able to measure any change in a sealed box

    However if the observer jumps( accelerates) himself in the uniform case he would find himself bouncing around in the box!! Normally this case is not explained. Galileo retains a gravitational acceleration orthogonal to the motion of the box. Because ballistics resolves the motions orthogonally one forgets that the effect of uniform motion is already encapsulated within the ballistic model.

    The moving observer must have sight of the fixed frame to make any adjustments required in ballistics.

    However for a box moving against or with the acceleration of gravity the experience of free fall is as described above.

    Now in the case of an accelerated box moving with the acceleration of gravity orthogonal to the gravity of earth the observer on launching himself would notice that he would be attracted to his rear as well as falling down this experience is best related to falling in a bus , not an elevator. Thus an observer in a sealed box would be able to tell whether he was moving orthogonal to the earths gravitational field.

    The principle of equivalence depends on direction of application!

    So now to the application to light. . Within a sealed box light would be affected in the direction orthogonal to the earths gravitational acceleration only if light was a gravitating mass! Thus the so called photon would not by definition be affected, but the so called electron would be. . But let us just consider light as a bulk property of the air in the box at a given frequency, then we may first understand that the air would become denser in the orthogonal direction of the acceleration of the box such that the propagation of light would be affected and refracted by this density change , as a consequence of the acceleration.

    To therefore expect light to bend around a gravitational body is not due to photons being affected, but the bulk material propagating light being affected.

    The curvilineal coordinate system of space- time thus properly reflects the dynamics of a bulk materiality such as an aether , and this is what Einstein meant it to do elegantly.

    Space-time is a mathematical aether analogue not well understood. It's curvilineal application to mathematical scalar fields for electromagnetism etc, reveals nothing about materiality, it merely reveals the nature of our schemes of measurement.

    When it comes to defining mass in such a system of course setting it on an earthly standard by no means guarantees universality!

    The only universal power we are aware of is through rotation, and of course that li is directly to magnetic behaviour as a universal on which to base logical measurement schemes.



    Why tidal forces measure the variation in the gravitational field and the limited application of the principle of Equivalence.


  • Boscovich's theory is validated over and over again by modern scientific measurement techniques!

    The variation in the interactive forces within materiality lead to a region in second law of Newtons Principles for Astrologers. What that men's imp,y is we must include forces other thn locally measured gravity constants into our understanding go the Olaf system and astronomy in general.

    The problem of action at a distance thn has a simple solution which I will address in another post. Suffice to say trochoidally dynamic surfaces lie at the heart of this solution
  • Bohr,Örsted and Boscovich, are hardly mentioned together it seems

    http://www.informationphilosopher.com/solutions/scientists/maxwell/action_at_a_distance.html
    And yet it is without doubt these 3 who steered Newtons Principles for Astrologers down the path toward a complete theory of everything.

    It isvBoscovich's theory of force that underlies the edifice of Quantum Mechanics ,tha Bohr was at pains to erect in the face of Classical Newtonian Physics as championed by Einstein both Bohr and Einstein lept fom Örsteds discovery of an intimate connection between the powers of magnetism and of electricism , in full and vibrant harmony with the Natural Philosophy of Gilbert, Boyle and many others intrigued by these active principles in nature and Alchmy .

    And yet it is as if the plethora of overwhelming insights released by Boscovich, we're whipped out of the hands and minds of Naturl philosophers by the extreme exigencies of war, upon revolution upon war, conquest and instability in Europe. .

    The secrecy. And the technological advantage in war of these advances lead to a European wide propaganda strategy that obscured what could be known and utilised by artisans, and left expertise in the hands of a handful of men whose insights have driven western technological and industrial achievement.

    It is the Boscovich theory of force, the discovery of that fundamental force in magnetism by. Örsted, and the pplication of that fundamental force to materiality by Bohr that not o ly completes the theoretical work of Newton, but also reveals the active principle he sought to uncover through Alchrmy . That principle is the magnetic dynamism in all materials
  • I now see what I had hoped to see in Maxwells paper on lines of force , explained with genteel clarity, and in honour of Faradau, ampere, Örsted and Boscovich.

    It is a fact of recorded history that Maxwells views were ignored or attempted to be buried by his olleagues particularly Kelvin, for a number of decades possibly 2 . As is the case in academia, you have to defend your position, and are wise to build a team of which some should be henchmen around the seat one occupied. . If someone seeks to overturn your seat then woe betide the!!

    Of course those out in left field often come in to take the prize, and thus the underdog becomes the popular hero , as ll is fair in love and war!

    The point is that trochoidally dyn,ic surfaces is the theoretical path to follow and the definition of curvilineal force embraces the conundrum of action where matter is not, or in spite of matter being present as a hindrance.

    The magnetic theory with Faradays lines of force involved intimately with virticity is revealed as the opinion of James Clerk Maxwell as a necessary extension of Newtonian principles via the theory of Bodcovich on how pressures interact with force laws as a consequence! .
    In this view it is not the discovery of the medium but the discovery of the laws of the action of the continuous medium that are scientifically of consequence and advancement. We may never turkey know the medium , and that in fact does not matter, for what matters is the laws of action exhibited by the medium , and any analogous medium may thus corroborate our understanding

  • Magnetic pole drives an interstellar flux xxx
  • edited February 4
    https://geometrydude.wordpress.com/2012/12/22/cavendishs-phenomenological-derivation-of-coulombs-law/
    The Hetoes of science often are overlooked in professorial presentations, leading the student to an unhelpful imagination of the natural philosophy and creativity involved.

    Cavendish not only developed the law of Coulomb, he backed it up with reams of data.

    But what shall we say of Faraday?

    James Cletk Maxwell was enamoured of him and of his insights, and yet he was subject to academic and societal pressures that curtailed his intuitive insights drawn from Faraday. Thus he uses the concept of centrifugal force incorrectly to describe the lateral spreading of lines of force, and he rushes to connect Hrlmholtz and Kelvins vortices with these magnetic lines of force displayed by iron filings with paramagnetic properties.

    The very nature of the lines he claims show at once the dipole field that is calculable by theory , but is far more pregnant than any theoretical model. Because it is a dynamic reality before the observers eyes. . Thus we see imposed on Faradays observations the nearest match to it from scholarly academia. It was this imposition that Faraday objected to.

    The natural philosophical position held by Faraday inspired by Boscovich, could not be reduced to iron filings emitting physical force lines or even a bar magnet emitting physical force lines. And yet the employment of these symbols of alignment of behaviours did avail much.

    In his deeper meditation he felt that the action of a power was revealed, not the emanation of lines of force! That being said the mathematical model draws some credence from this settled dynamic pattern, but no validity.

    If coulombs law could be made time wise dynamic the results would evidently show that it is an inaccurate depiction, having relevance only to the steady state system. The inclusion of vortices by Maxwell only serves to complicate an inaccurate rule.

    It is not until the finite element model is employed that results offering dynamic similitude are obtainable. That is to say: numerical fluid dynamics can deliver better approximations to the iron filing patterns than coulombs law or Maxwells lines of force interpretation .

    Nevertheless, the radical nature of his connection of rotation to magnetism, electric ism, and light, and his clear explanation of a field, and his subordination to the action at a distance camp are steps toward a mathematical clarity which enabled the finite element model to attain to its level of usefulness after so long a time!

    It is the case that impressive though the mathematical formulations are, they nevertheless failed to illucidate what was observable. Indeed all mathematical depiction is indeed an enunciation of a natural law not a revelation of it.

    Those who by careful measurement in experimentation find some invariant proportionality can not nor should they claim universality of application, nor indeed accuracy of depiction.Rather repeated application of the proportionality may serve to convince of the pragmatic utility of it and it's limitations . The expert may then draw from experienced observation which tool, rule of thumb, or law to apply in his endeavours, while others may endeavour to create or discover even better rules and methods of proportionality.

    Key to this endeavour is the acceptance of curvilineal lines of Fotce, but also an understanding of what a force is and how it may be depicted by a line straight or curvilineal
  • edited February 4

    http://www.eoht.info/m/page/Roger+Boscovich
    When Volta attempted to put forward this idea of the dynamic duality in attractive and repulsive force regarding the electric spark, he was severely reprimanded by his local university professor, who was a Franklinite and believed only in electric repulsive forces. The instability of such a system is obvious with a little thought in the same way the centripetal/ centrifugal system Newton used to explain orbital me Janice's require a motion to work against to obtain stability. That motion was in fact a varying tangential velocity which produced the opposing force to the centripetal/ centrifugal force. In the case of the centrifugal force the moving orbiter itself must resist a circular obstacle by its own elastic body force.
    Le Sage went to great lengths to demonstrate a corpuscular collision model akin to a pressure surface model, but failed to convince his colleagues because of the complexity. A fluid dynamic interpretation by Newton had also produced unsatisfactory results, due principally to lack of knowledge of fluid behaviours, assumption only of a resistive nature in their application and inadequate computational aids for the massive task at hand.

    Boscovich, by combining forces rather than distinguishing them was able to give a satisfactory account of all natural phenomena . It is of great interest that Cotes work on the use of the imaginary magnitude contributed to a greater understanding of how these forces may be combined usefully.
    Indeed the binomial expansion itself suggests combination of forces to achieve a simple effective Force law

    However much is yet to be learned from consideration of the cause or medium of interaction of force.
    https://en.m.wikipedia.org/wiki/Roger_Joseph_Boscovich#
  • One can NOT apprehend what Einstein was attempting to do regarding Gravity without first starting with Newton and then apprehending Biscovich. Boscovich's principle of impenetrability ensconced action at a distance within a field. The concept of a field is hardly explained be ause it is deemed too mathematical to explain, but in fact a field is a field in the common sense. It is what is contained within that field that is of usual significance .

    The conception of a field as a field is then extended to that of a specified volume of space , and then finally into many dimensional descriptions based upon that volume.
    Space- time is such a generalised field. What it's contents are determine it's significance. Einstein never excluded the concept of an aether within his field, even though he excluded some expressions of what a luminiferous aether might be.

    In fact we know he was enamoured of Maxwells tentative concept of a medium or aether that might be called electromagnetic. It took some time for him to make that clear , because generally Maxwell was held in poor regard in the theoretical community .
    Until Heaviside and indeed Einstein, few but the Maxwellians came to appreciate the significance of Maxwells Theiry. By then Maxwell himself had been forced to redact his original theory several times by Kelvin and his Cronies. His work was shorn up as best as he could, although his original conceptions were in Tatters! He had nailed his cross to Hamiltons Quaternions and was made to pay the price for being in advance of his academic superiors!

    Bill Clifford was the next labourer in the field prior to Einstein, but the general thrust of Biscovich's theory of forces or powers was behind it all
  • What is force?
    Perhaps it is better straight away to point out that is the wrong question in the post Newtonian era. HowevervBoscovich was in the Newtonian era and the question was far from settled? In line with Boscovich Einstein asked " what is gravitational force?
    His answer was the theory of General relativity


    Because you probably have not read Boscovich's theory of force you might not be aware of the curios nature of our concepts of force .
    Gaya is the Sanskrit for meal or strength. . It is that sensation of revivification that spreads through the body as a meal is digested and distributed throughout. This is the indo Europeannroot for the Greek andvLatin cognates " is" and "vis". That ebullient energy and bustling vibrancy that exudes from a healthy animate or plant,

    We sense this inner strength and resilience, the resistance to life's knocks and bruises, the repulsion of all objects and animates that attempt to overpower or block the growth, motion or expansion of that vibrancy.

    When it is applied to some end it presses up against many things and strains to move them out of the way! Sometimes it seems effortlessly to achieve its intentions to remove obstacles and to overcome resistance, other times it seems only to react to objects pressing up against it.
    And it comes from within an animate after a meal!

    But this exploration of this energy would be remiss if it did not point out the much greater overwhelming energy of wind, and river and moving earth in an earthquake. Against these animate energies pale into insignificance. And what "meal " feeds them?

    When it was common to anthropomorphise all of nature, to attribute powers to invisible gods and various underlings, djin, daimons and other agents the meals they ate we're often seen as sacrifices that may or may not have causative effect, but later it became clear that these were myths and fancies of the wise to control the masses of uneducated or educated but unwise people , the nature and origin of these powers were allowed to recede into the Nature of that which is around, as resident powers or ordained edicts.

    Newton thus provided a beacon to the wise: to lift their minds from the morass of theory, theosophy and speculation into the clarity if measurement, and then from measurement alone to determine what true law their may be in terms wholly of proportions.
    This wasvthecway of the Pythagorean school.

    And so by Galileo the power that observed ruling the heavens was but by but revealed, while on earth the powers by Archimedes revealed and by Timaeus, and others were shown to be in inviolate proportions.

    That these powers were called vis in Latin does not, by Latin make them Newtonian forces! In fact Biscovich and Faraday andvNewton were not confused by the term vis and. Newtons and Galileos proportions for gravitation and its effects on bodies.

    It was also Boyles and other Alchemists experience that such powers not only inhabited materiality , but exhibited in many forms besides gravitating!

    It was by considering these other evidential behaviours that Bidcovich and others came upon a general conception of forces in nature, which were far from being constant , that is in constant proportionality.

    Newtons second law was and is part of his Astrological principles for the motions of celestial bodies both on the surface of the earth and in the depths of space. But everyday motions did not show constant or even uni directional motion!

    The results of Boscovich's investigations were the many differing motion laws he depicted .in his theoretical figures.

    Boyle demonstrated that thevpower within materiality was what was called a Pressure. It. Was this pressure that pressing against an object exhibited the power from within, the vis (or force) of the material under investigation . That pressure or vis was repulsive at times and then attractive at others, and the magnitude of that energy was captured by the surface enclosing it. By allowing that pressure to move a small part of that surface a measurement of the vis of that material in those conditions were obtained.

    But Newtons theoretical model defined force by gravity, so all vis was standardised against gravity, that is pressure was described by an equivalence to gravitational vis. Gravity was not thought of as a pressure inward , but as an entity called a Newtonian force distinguished on its own by a formulation.. It was the formulation of the gas law ratios and the formulation of the gravitational law ratios that dominated the conceptualisation of force as Newtonian force rather than an expression of innate material powers.

    These innate material powers had barely been investigated when scientist began to equate and explain them by Newtons gravitational model. Faraday was furiou with Maxwell for obscuring this distinction, for misinterpreting Biscovitch and for selling out to Academia rather than to direct observation of these mysterious motions.
  • Boscovich's law or conception of impenetrability derives easily from the Struct interpretation of Leibniz Monads. Being a mo ad it may never combine to become a Fuad, although it may associate ith another no matter how close. The powers invested in monads may be Herculean or slight, but no monad my be overcome by another so as to subsue it. Thus even if a point was invested with inverse square law powers of attraction at one point a repulsive power must exhibit to prevent the monad from coalescing with another.
    Thus, while material bodies provide a theoretical difficulty of locating the centre of cause , and therefore action at a distance is confused, both Newton and thus Boscovitch endowed a monad with requisite powers to fulfill it's observed condition. That monads became called points or Punkte is not to be confused with the geo etrical point, but rather the Pythagorean seemeia are referred to. Thes being distinguished monads that communicate some area or volume or region of interest to an observer, and indeed they are monads, having no part .

    Yet to invest a monad with distinct powers is to invoke a partition of influence if not of body.

    It may be that monads are also singular in their powers, so that a combined power at once indicates several monads of differing powers are involved.

    We might then admit that an attractive monad is combined with but not penetrated by a repulsive monad , but not necessarily of the same or inverse law., and only the theoretical law of impenetrability prevents them from merging into one weaker monad.

    In fact we seem to see this law in the dipole of a magnet , so that thevBloch wall is evidence ofbsuch a contingent principle, which otherwise might be seen as convenience on the theoreticians part.

    Thus we may explain properties of materiality by these ki ds of Boscovichian monads in a way that makes magnetic dipole behaviour fundamental to all materiality.

    We on fact need only the notion of powers attributed to distinct points to establish a material volume and it's othe measurable properties.

    I make one proso: that monads are not necessarily points in space , but that points may be assigned to a monad as its centre by means of its rotational curvature , and motions whose origins may be assumed as given

    How then do monads I teract on monads, or rather how do rotational forces combine with other rotational forces 0r powers,

    The solution is in returning to powers interacting the pressure on a surface seems a good combinatorial structure to exhibit combined effects of a system of monads exerting their influence at some distance.

    Impenetrability should therefore be regarded as the first principle of action at a distance
  • From Whence comets motion?

    If one supposes monads with singular force laws either attractive or repulsive of other monads with the principle of impenetrability then by some undeclared time one might expect a state of equilibrium to be achieved, anD all motion as it were to cease, and a dipole universe to be thus established .

    However, the observations suggest something a bit more subtle . The motion of monads is in perpetual, that is fundamentally the monads form a perpetual motion system which first moves one way toward an equilibrium for an indefinite time and then moves another way and so on.ed Lorenz water clock illustrates this dynamic aperiodicity.

    At once therefore the monads are assumed to move each other in circular motions about any monad, that the laws of attraction and repulsion are not merely centrifugal/centripetal versus anti centripetal/ anti centrifugal, that is to say directed to ir from a monad by attraction or repulsion whether it be by some " string" drawing in or some wall bouncing in or some rod pushing out or some shell bouncing to but by some power that encourages the monads to circulate about each other.

    Given this principle it becomes clear that monads may be fully determined by a system of circular powers , which is to say that circular powers may equally describe what is observed without the need for any substantive monad to " exist" , so that the great mystery of motions may be usefully conceived of two circulating powers of opposite spheroidal circulation, and therefore not confusable in any way , as is plane circulation , with variable diametric components , when resolved into components , may sufficiently be the basis of all theoretical motions in space.

    With such a proposition, one may unify all observable behaviours and powers of motion and indeed see pressures as the birthing place of all Newtonian forces, that is to say all gravitational forces, and many other forces besides including magnetic and so called electric forces and vibrational forces of bth sound and heat. And the weak and strong nuclear forces, so called.

    While it is necessary to propose such a spheroidal ly. Dynamic basis for all motions it is not sufficient to assume simplicity in the combinations of such monodic equivalents. Indeed ar every stage a requisite complexity should be assumed, and simplifications only used for purposive clarification, not final judgement.

    So as a case in point, Newton declared that vortices as far as he could determine played no role in the options of celestial bodies , because his system was not capable of resolving the asides of the moon!

    However he did allow future generations to try to do better than he was able to do, as the necessary complexity of his project was computationally beyond his lifespan! . And similarlybMaxwells formulations were like Syokes and Naviers beyond complex solutions until ClaescJohnson applied the Finite Element model to the task.

    And now we may see what Einstein and Minkowski observed, that motions around certain curved spaces behave similarly to forces acting on other other forces in our reality. In particular angular momentum may be retarded or enhance in proportion to an analogous motion in a specified "curved " space.

    This is a mathematical ormalism, an analogue that provides solutions to real world situations involving gravity by recasting the situation in a geometry with the correct curvature.

    Is our space really curved?

    The answer is yes and no. Yes because we can find physical examples to explain the geometrical concepts we wish to employ to do a calculation and no because we can recast the situation in spheroidal dynamics in our accepted Space.

    At one time the church insisted that space be Euclidean , but now we know better that space is in fact a fractal geometrical conception which excludes no conceivable geometrical analogy. Thus curvature of space is the least of its properties in our conception!

    I might add, with regard to relativity, that Aristotle reasoned that all motionscarevrelative to each other, but that if one must have a cause for motion, then it must necessarily be a "Prime" mover. That is to say that there exists nothing before it to cause it to move! Therefore it moves everything else and itself, but nothing else can move it.

    Such a prime mover is not necessary , but it is sufficient to explain all causation in motion. It is however not perceivable by anything it moves, as it may also move itself . It is entire to itself and absolute in the Latin meaning of the word, utterly independent and alone , unaffected by anything .

    The usefulness of a prime mover is in providing an absolute reference frame. Such a reference frame being absolute means every other motion can be measured against it, for the motions do not affect it. . But we see clearly that this is the realisation of a desire to have absolute certainty rather than an effulgence reality discernible by spiritual insight! . Relativity merely says ; when deciding upon a reference frame, no account of some third mythical absolute frame is necessary. The observer can choose which frame he wants to set as absolute.

    Then general relativity tackles the issue of choosing an acceleratin reference frame as absolute. In such a case it is the principle that gravity and the accelerating frame are indistinguishable. .

    However tidal motions obstruct this simplistic view in a rotational reference frame that is accelerating rotational ly or simply moving with constant angular velocity. . This is because angular velocity resolves into a balance of attractive and repulsive centrally active forces from a pressure or power of circulating motion.
  • edited February 6

    A better definition of curvature






  • The equivalence principle is a guide to constructing tensor equations! And once formed the equations represent space which is non empty, that is gravity / density have to be taken into account. To isolate gravity as causative is to naively assume that materiality is not an indissoluble component of all physical quantities. Just because we forget materiality in forming our equations by concentrating on one behaviour, does not by fiat divorce that behaviour from its physical reality, ie relation to characteristics like mass and density and permeability and susceptibility.
    Thus Einstins theory assumes a material aether with the requisite behavioural constraints, that is rotational notion cased by pressures wor powers within the aether.
  • edited February 7
    One of the difficulties for Einstein was creating a language for space time that did not involve Quaternions and vortices.

    Because he focused on the gravitational field he missed out on an important dynamic: the dipole magnetic field. As a consequence his general theory lacks one of Boscavich rules of force, and that is impenetrability. The consequence of this is his geometry allows singularities.
    Quantum mechanics however follows Boscovich more closely . The quantum themselves are monads that are allowed to combine but not penetrate. As a consequence Einstins theory does not blend well with quantum mechanics.
    The solution is simple: add a vortex term onto the energy tensor side, and impose strict impenetrability rules.

    Maxwells original equations deal with the strain in a medium of vortices. This should be the energy tensor side from which the CavendishnCoulomb law should be derived , corresponding the geometrical curvature to these set of onstraints, and then from that model driving the gravitational law of Newton.

    The quantum restriction on applicability and indeed on the force laws , requiring a dipole moment would carry out Boscovich's programme and reduce the computational burden, and unify quantum dynamics and gravitational general relativity.

    Diracs equations and analyses then could be given not just a probabilistic interpretation, but also a hyper geometric one and the rotation would be em ended in the conic section curves .
    Nasdim Haramein added a rotational term to accomplish this, but of course that is one model among many.


  • edited February 7
    If , like me you were labouring under the illusion that forces or more fundamentally powers of motion only act in straight lines , and that this is a divine law discovered by Newton, consider the facts.
    Firstly Newton accepted and used curvilineal forces.
    Secondly in his principles for Astrologers he acknowledges ordained curvilineal forces for celestial bodies in motion
    Thirdly he speculated if circular motions and forces were not in fact absolute motions! Absolute meansbasbit always has, utterly independent of other influences.

    For all students of the circle it is accepted that this locus is prosy or prime, it can not be resolved into a combination of 2 other motions like lineal motion can.

    So...
    Why are we left with the impression that the circle is resolved into a tangential velocity that always varies with a centripetal force applied at every instant?

    This is not the case. If you try to create a circle in this way it physically does not happen. Instead one needs to transmit a wave down a tether so that at the point of joining the tip or whateverbiscattached a varying ly directed force is applied. The resultant of this is a varying directed motion that oscillates ,. By varying the wave and resonating the source ofbthevwave to a circuloid a circular motion is established in resonance at the tip!

    In steady state it looks like the velocity of the tip is driven by the rotation as the centre, but for a string if the resonance fails , the tip will not move in a circle, It may move in a spiral out of phase with the centre rotation.
    In the case of the case of a viscous tether such that stiffness in the material ofvthevtether is evident, the tether will bend in vibration until its elastic limit is breached and then the tether will undergo plasticity shortened by a violent fracturing of the tethering bond.

    So, supposing a mass to be at the end ofbthebtether I may describe a varying pressure on that mass that "pulls" the viscous lump in wearying pendulum like directions, accelerating the mass first away from the centre and then toward the centre while moving around some mean tangential spiral , providing the wave in the tether is maintained .

    The wave in the tether at first is in tension in one direction and that tension is shaped by the wave in all it's directions. The relaxation in the tether returns a relaxation and compression wave allowing the mass inertia to continue its motion until the next tension pulse arrives to alter its course.

    These pulses of tension are variable not only in magnitude but also in direction. Providing a pressure in the mass that varies in its resultant.
    The rule that the resultant might be depicted by a straight line is in fact an aid to imagining how what is a curvilineal Fotce acts at each moment.

    We therefore reduce these mo entry pressure variations to that of the tangents to a wave curve as it impinges on the mass inducing a " pull" pressure, and a negative relaxation pressure in the direction of the inertial motion. The resultant of these two pressures is an outward motion which restores the tension in the tether so that the next wave might pulse or propagate through.

    The system reaches a steady state only when the rate of wave pulse propagation and the angular momentum of the generating end achieve a resonant frequency. In that case the tether appears to be in a standing wave configuration and the mass moves in its true curvilineal path under a combined forcing wave and mass inertial system .

    The system is maintained by a curvilineal force that accelerates against any environmental decelerative forces.

    When the steady state is achieved and the standing forcing wave, itself rotating through space in a surface akin to some co e of a certain apex angle, which angle varies by the curvilineal acceleration of the mass, we may describe its positions using Pythagoras ratios of the right triangle, and other circle properties.

    Thus if it's position in time is given by cost, sint, then its velocity in time is given by
    - sint,cost and its acceleration in time by - cost,-sint.
    You may see by these formulations that a circular motion can not be started by pulling on a tether! And yet we do this without thought, and this is because the steady state assumes a starting velocity , which I have described as a product of a wave transmitted along the tether by which the forcing centre achieves with care a resonant frequency.

    We may also see that the forces or accelerations as resolved components vary in such a way as to point at the centre , but in No way to stabilise the system. We need to add counteractive inertial forces to maintain a circular orbit and such forces are NOT centrifugal, but rather counter centripetal/ centrifugal inertial forces.

    Now these forces, the centripetal and counter centripetal may be resolved into a continuously varying tangent like force which indeed is none other than a curvilineal force described by components that vary in time .

    Such curvilineal pressures exist and are witnessed everyday in fluid motions. It is the obscuring of them by those who believe only in rectilinear forces that has been the issue.

    However Ampère at once realised that they could no longer be denied, as was the fashion of some great minds and it is these curvilineal pressures that form the Basis of Boscovich's theory of forces, by means of Leibnizian monads that posses properties of action at a distance by them.

    It is equally satisfactory to assume that curvilineal forces generate points of rotation as to assume points generate curvilineal forces about them! And in my opinion, it sets a firm foundation to proceed from curvilineal motion to points than the other way round xxx
    One last thing we may observe about inertial forces: a mass in motion has by Newton a quantity of motion. This motion is inertial and therefore requires force to alter the quantit and the direction. This quantity is called momentum in modern speech and is seen as a derived product of differentiation. However Newton considered it an inertial force that took time to be abated.
    Thus the hidden force is the inertial one which acts in a resistive manner. When one restores the notion of a quantity of motion we restore the concept of inertial forces and we reconnect to the nature of volume as possessing resistive mediums within it. Such mediums explicitly avoided by Newton from the outset are reintroduced in this notion of inertia in mass, or materiality, whereby we make a better connection to fluis dynamical notions and viscosity.

    http://www.sosmath.com/calculus/diff/der03/der03.html
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