Re: vis-viva and vis-motrix

On 09/22/2024 11:37 AM, Ross Finlayson wrote:

On 09/22/2024 09:59 AM, Ross Finlayson wrote:

On 09/17/2024 11:41 AM, Ross Finlayson wrote:

On 09/17/2024 04:34 AM, J. J. Lodder wrote:

Ross Finlayson <ross.a.finlayson@gmail.com> wrote:
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Does anybody even bother to think about vis-viva versus vis-motrix
anymore, with regards to conservation, momentum, inertia, and energy,
and potential and impulse energy?

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Of course not. These are obsolete distinctions,
from a time when energy and momentum conservation was not corectly
understood.
The matter was put to rest by Christiaan Huygens
by showing (for particle collisions)
that momentum conservation and energy conservation
are distinct conservation laws, that are both needed,
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Jan
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Is it usually considered at all that momentum and inertia change
places with respect to resistance to change of motion and rest
respectively sort of back and forth in the theory since antiquity?
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Several times?

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Au contraire, there is yet definition up, in the air, as it were.
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Find any reference to fictitious forces and for a theory
where the potential fields are what's real and the classical
field's just a projection to a perspective in the middle,
and anything at all to do with the plainly empirical or
tribological with regards to our grandly theoretical,
and one may find that the definitions of "inertia" and
"momentum" with regards to resistance to changes in motion
and resistance to changes in rest, as with regards to
weight and as with regards to heft, have rotated each
few hundred years, as with regards to the great schism
whence Newton's vis-motrix, as with regards to the vis-insita
and Leibnitz' vis-viva, as what for example can be read into
from the Wikipedia on conservation of _energy_ and conservation
of _momentum_ up to today, where for example, the "infinitely-many
higher orders of theoretical acceleration are both formally
non-zero and vanishing" because "zero meters/second
equals infinity seconds/meter".
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So, for a true centrifugal, and quite all about the derivative
and anti-derivative as with regards to momentum, inertia,
and kinetic energy, in a theory what's of course sum-of-histories
sum-of-potentials with least action and gradient, or sum-of-potentials,
it is so that the various under-defined concepts of the plain laws
of after Newton, are as yet un-defined, and there are a variety
of considerations as with regards to the multiplicities, or
these singularities, and the reciprocities, of these projections.
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So, some of these considerations as since "Mediaeval Times",
help reflect that Einstein's not alone in his, 'attack on Newton'.
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Moment and Motion:  a story of momentum
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https://www.youtube.com/watch?v=DH-Gh-bBb7M&list=PLb7rLSBiE7F4eHy5vT61UYFR7_BIhwcOY
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Theories and principles, momentum and sum-of-histories
sum-of-potentials, conservation, momentum and inertia
and energy, fields and forces, Einstein's mechanics,
conservation of energy and conservation of momentum,
potential and fictitious and causal and virtual, mv, mv^2,
ordinary and extra-ordinary in the differential and inverses,
the standard curriculum and the super-standard, momentum
in definition, classical exposition, Bayes rule and a law of large
numbers, law(s) of large numbers and not-Bayesian expectations,
numerical methods in derivations, uniqueness results later
distinctness results, law(s) of large numbers and continuity,
complete and replete, induction and limits, partials and limits,
the paleo-classical, platforms and planks, mass and weight
and heft, gravitational force and g-forces, measure and
matching measure, relativity and a difference between
rest and motion, heft, resistance to gravity, ideals and
billiard mechanics, wider ideals, Wallis and Huygens,
Nayfeh's nonlinear oscillations, addition of vectors,
observables and ideals, DesCartes' and Kelvin's vortices,
black holes and white holes, waves and optics, Euler, both
vis-motrix and vis-viva, d'Alembert's principle, Lagrange,
potential as integral over space, Maupertuis and Gauss
and least action and least constraint, Hamilton,
Hamiltonians and Bayesians, Jacobi, Navier and Stokes
and Cauchy and Saint Venant and Maxwell, statistical
mechanics and entropy and least action, ideal and real,
mechanical reduction and severe abstraction, ions and
fields and field theory, wave mechanics and virtual particles,
ideals and the ideal, the classical and monistic holism, paleo-nouveau.
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Much like the theories of "fall", "shadow", or
"push" gravity, or the "shadow" or "umbral"
gravity and for theories of real supergravity,
as after Fatio and LeSage, as of theories of
"pull" or "suck" gravity of Newton and the
"rubber-sheet" or "down" gravity of Einstein,
then the theories of vortices like DesCartes
and Kelvin, and others, help reflect on the
rectilinear and curvilinear, and flat and round,
as with regards to deconstructive accounts of
usual unstated assumptions and the severe
abstraction and mechanical reduction, in as
with regards to modern theories of mechanics.
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Zero meters per second is infinity seconds per meter.
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You know, zero meters per second is infinity seconds per meter,
and, any change of anything in motion has associated the
infinitely-many higher orders of acceleration, and,
it's rather underdefined and even undefined yet very
obviously clearly is an aspect of the mathematical model,
that Galileo's and Newton's laws of motion, sort of are
only a "principal branch" as it were, and, don't quite suffice.
Of course anything that would add infinitely-many higher
orders of acceleration mathematically to the theory,
of mechanics, the theory, would have to result being
exactly being the same as Galilean and Newtonian,
"in the limit", and for example with regards to
Lorentzians and these kinds of things.
It's sort of similar with adding more and better
infinities and infinitesimals to mathematics.
The continuous dynamics of continuous motion
though and its mechanics, is a few layers above
a plain concept of the continuum, as with regards
to something like a strong mathematical platonism's
mathematical universe, being that making advances
in physics involves making advances in mathematics.
Which pretty much means digging up and revisiting
the "severe abstraction" the "mechanical reduction",
quite all along the way: paleo-classical, super-classical.