Re: vis-viva and vis-motrix

On 09/27/2024 05:52 PM, Ross Finlayson wrote:

On 09/26/2024 01:41 PM, Ross Finlayson wrote:

On 09/26/2024 10:39 AM, The Starmaker wrote:

Ross Finlayson wrote:

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On 09/25/2024 01:55 PM, The Starmaker wrote:

Ross Finlayson wrote:

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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.
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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.
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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.
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Which pretty much means digging up and revisiting
the "severe abstraction" the "mechanical reduction",
quite all along the way: paleo-classical, super-classical.

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"zero meters per second is infinity seconds per meter"????
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Do you guys even have any idea whats yous talkings abouts?
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'infinity' has no time and cannot be measured. So, that means there
are
no 'seconds' in "infinity", and no meter/meters/inches in "infinity'!
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In "infinity" there are no meters or seconds.
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Where do you guys get your information from? Albert Einstein??
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"Moment and Motion:  infinity and large numbers"

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Oh i see, yous people live in a Mandelbox universe...
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i wasn't refering to yours 'numbers' universe..
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i was refering to the real universe.
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Einstein said he wasn't sure if the universe is infinite or not..
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but I'm sure the universe is infinite...just not the one you're
in...only it's surrounding universe that yous are expanding in.
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sorry to bust your bubble.
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Actually, there's an idea that one way to conceive
the universe, is, as a mathematical continuum, that
these days that's what's called "holograph", or "hologram",
the idea that one mathematical continuum is big enough
to have a number, for each thing, and relation in things.
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Then these philosophically are called "plastic numbers,
metal numbers, concrete numbers".
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Then, for example, Euclidean space, and, maybe not
Minkowski space, have it that there's only a ray
of time, or 3 + 1/2, with three space dimensions,
rolling and curled up, in the infinities and the
infinitesimals, one continuum.
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It might even be reasonable to explain sort of why
there are three dimensions in a mathematical universe
of the space-like, simply courtesy properties of numbers,
because "least action and a gradient" is about the
easiest way to say "it is what it is, and it will
be what it will be".
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Then these days it's most usual that people just "add"
dimensions like in superstring/supercorde theory, yet,
that's just some scratch-pad, when the cosmic clockworks
makes its own book-keeping, about time-series data dense
and brief, unique discernibles as sparse and varied,
and combination tuples as of their own sort of topologies,
while the continuous manifold of Space-Time, has its
own sort of mathematical, continuous topology,
why it is so.
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Then usual ideas like non-Euclidean geometries
and fractals are sort of a mental playground,
while a "real spiral space-filling curve of
a natural continuum", sort of provides Euclidean
geometry for free from first principles.
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Applying Torque and Driving Torque
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There is making a turn while walking,
and immediately making a 90-degree turn,
while holding 90-degree's either way how much,
that the alternate route is as close as the current route.
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Then there's whether straightening-out or
turning 90-degrees the other way, when
for example when walking a path,
turns have the feet going in different directions,
or side-stepping.
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It's like "on the sidewalk you can always go out of your way",
stepping around and past and to, with stepping
and stopping, walking.
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Then it is as to where the actual guidance
of the path, is direction when walking,
the angle to make shortest angle when
instantly comparing a path, with an
alternate, with respect to destination,
formally at the end of the path.
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It's figure that walking is in paths,
then with "torque is in quarts",
then "quarts are in cubes", then
as with regards to sub-atomically:
"torque is in quarks", angular torque,
as a static concern when "torque is static".
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Quarks are in fields, ....
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I.e., here the torque, in quadrants,
torque of the walk, is forward/stop
left/right, forward and side-to-side,
in terms of that "quarts are in cubes",
reflecting that as a "four-volume",
meaning simply only an equi-partition
into 4, that the graphs where cubes
run out, for power in size, reflecting
going forward and left to right,
what arrives, at stops then as what
results when, how and whether stops
restore inertia, from its virtual sense,
again to "rest frame minus direction".
Then direction is included, that direction
always includes the inertia, "displaced
inertia", what results equilibrium, "free-free",
next decision in direction.  (Feet.)
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This is where it's figured orientation is
either standing or face down, at rest
or moving, either or both feet.
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This way it's a simple model that lives
in machines, a complex machine, two feet.
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Here's a thought experiment, for example,
"tripping".  If a step is too high and encounters
a trip, then there is either tripping to face-down,
standing, or otherwise choosing the next destination.
Face-down involves walking, standing involves stopping,
and choosing involves not tripping.
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Then there's stepping, for example, establishing
any change in height, vis-a-vis grade, and stepping
up grade, where on steps, it's figured height is
average 45-degrees up, left-per-right, while driving
is _maximum_, where for example a lift might be
straight up, a step.  Uphill grade is step with regards
to making or maintaining power up the grade,
feet on grade or wheels on grade.
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Then the idea, for example, to always have the forward
free/free left/right, "in quarts", is that a gallon, is a unit
cube, and quarts, mean an edquipartition, where the
quarts are in the direction of the flow, of the walk power.
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Then each adds and makes magic squares when walking,
random,
and accordingly turning left and right, and usually not
turning, in turning by stepping when stopped, step
and side-step and turning shuffle, eg the two-step shuffle.
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The idea is that "magic squares", divide the torque into
cubes, that it is in eights, vis-a-vis, that "quarts", in the
model, make the cubes or in eighths, in terms of
power versus mass ratio, between squares in mass
ratio and cubes in mass.
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Then usually the rest of the dynamics makes "flow",
as with regards to it being only one-way, as there's
only standing and face-down, magic squares, and flow,
that it works out the cubes, in "lift, step, and grade",
uphill and not face-down, then for example as with
regards to downhill, and gradient descent according
to current path and future path, where the decision
according to drive, results that starting and stopping
in drive are power train, while walking are that steps
are free, standing and walking (and stepping).
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Then the magic squares, where adding up any
row and column make the same numbers, has
that they can be any size how many numbers
in the magic square, that for the larger the magic
squares, how those add up makes "the density of
magic squares in grids is small", yet, "power flow
transfer", changes grids freely, dense/least to sparse/most,
magic square flow, while still that it is free in the flow,
and only a continuous transform, from real flow to
real flow, the anti- or reverse "flux" the flow, just pointing
out that magic square to magic square, sitting where
the quarts are linear transform being maintained in parallel
overall, has that going straight it's also the same,
while there's always formally turning, the 'as far out'
next square, is whatever none zero of those averages
out as ringing, in as regards to ringing and out.
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That is to say, a magic square flow, as cubes, is
two magic squares coming and going, while
the torque vector, is a four-vector, is moving quarts.
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Driving is about same with power, drive, and
train, resulting turning is a higher exercise
with steering and power steering, while
"walking and step is zero power", the idea
that the steps are free.
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Then, "torque is in quarts", is just a convenient
way to say that steps, usually make for that
being "inertia-less", in terms of that standing
results both feet stepping at once, non-zero,
then standing, while walking is both the "both
feet standing at once, at stepping", and the
"one foot standing, one foot stepping", the
entire otherwise contribution of the main stress frame,
then where running is drive, and for example jogging
is walking and running, either way up/down.
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Here the feet are always moving in different directions,
for example with stepping, and walking, where the
steps set in the same direction, left/right, here where
the left/right are let out on the "torque squares",
where the quadrants of the quarts, have left/right
and the not-falling-down, steps left right and up and down.
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Steps are usually picked down before up.
Then otherwise is being able to stop the step on the way up,
otherwise "overstep".
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When both feet are in the air then the only way to step
is "over the stop", as with regards to the half of the plane,
the quadrant's quadrants, in the "magic square flow",
where it's the properties of numbers that result "in magic
square and laminate and toroidal flows, the 'different series',
have the magic square difference series 'potential in torque'",
the applying torque and driving torque.
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Then, there's "quarts and quartz", not really relating,
quartz time and quart equi-partition, that a quartz time
is classical in effect in time-keeping, a perfectly accurate
quartz timer is figure that temperature-controlled oscillators,
result that quartz time is classical as kinetic, vis-a-vis the
digital quartz, representing quartz as dielectric, the usual
idea of that with regards to power, that clearly the paths
share the same clock.
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The clock might go slower than one or the other,
yet then they wouldn't be the "equivalent paths"
with regards to destinations and differences in
outcomes, any one or two paths, when estimating
or changing direction.
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I.e. then it would be as for "turning 'on the dime'",
as with regards to power, that "steps don't turn
the other" and "drive does turn the earth".  (Non-zero.)
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I.e., the walking turn is free then free/free or changing
the direction and powering up and down, while the
drive is free to keep going while driving in steering,
that steering is free under power and wheels.
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Then, "magic square flow", has then for that it is
what results that minimizing, differences, happens
both before and after in step or while driving, while
walking then either makes stops or doesn't make stops.
The laminar and toroidal flow work out in those,
layers usually or wash, corners.  This then is for that
corners, whether turn is turning or not turning,
corners are turned, while as with regards to closing
corners, and making changes, that it's laminar in
one dimension and also the same toroidal in that
one dimension and also the magic, flow of the object,
walking or being driven.
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Then that works out to that is as above the costant
turning over time, which in steps in free while in
driving is turning-radius.
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The reason "why quarts", is because "liquids slosh",
then with regards to the kinematic is amorphous,
a standing body with feet and momentum, has that
slosh in the sense of "moving feet, or, feet pushing
on the ground", has that standing up is under slosh,
as with regards to "slosh", being that solids don't
slosh while liquids always slosh, while turns slosh,
that in walking all slosh is contained via the center
of balance, while in turning slosh is out and tractive.
Then the constant inputs what result "drive is
input on the train", is about whether it's feet
or wheels, making centripetal and centrifugal,
as with regards to that under wheels and running is truck,
with driving under wheels, while walking is also
rolling freely, stepping under foot.
Then it's that keeping the traffic is fishtail and slosh,
with fishtailing and slosh and wiping out, vis-a-vis
walking or running and side to side or unbalancing slosh,
that liquids wash and it makes slosh, then for example
that a kinematic body, has an abstract center of motion,
of a spherical liquid centroid, though it's the shape of
the upright or standing body, that also it's the shape
of the moving body, with regards to all the kinematics
centers or centers of rotation, as those all orbit while
either leveraging or floating each other.
Then, collisions, seems sort of result when there's
momentum, and energy, and those about the derivative
terms, that acceleration, is out into squares, while,
the power ratio, is out into cubes, that being classical.
Then, there's incident and there's follow-through,
with rigid and the stress tensor, "kinematic", and
"kinetic", or "wreck in motion", "meeting in motion",
otherwise "orbits, while tracks", that passing is
always peripheral, about "equal and opposite reaction",
something about that being "crashing" or "glancing"
or "missing", passing, then "passing apace" or "passing opposite",
then I suppose there's "t-bone" or "crossing", here just
pointing out collisions, have two decisions involved,
where otherwise there's the idea that the steps of
walking and the steering or driving, as moving massy
standing and walking and running and driving bodies,
has either "there are no head-on collisions" or "they
are all head-on collisions".
I.e. it's figured usually enough that collisions cause
either wrecks or falling face-down, not usually carrying.
Here the point is momentum, what's being conserved
is the centroid, its potential to be walked or steered,
also what's being summed, that the potential in running,
has the static torque and the static inertia, "conversed",
with the completed un-deformed, and not re-formed,
and the completly deformed, and re-formed.
I.e., the formation otherwise on the main lever or mover,
the feet or wheels their contact and into lift and riding,
has for the wheels and feet in motion, that the body and
cars are or aren't in motion, with respect to the wheels,
or feet, it's figure that individual motive force and power,
of a walking or rolling body, according to power and force
to the ball or wheel, of the foot or wheel, it's figured applied
drive or not, motion in bodies besides idling.
Mostly this is about making turns and turning, and
making turns and constantly turning either way,
instead of resulting making turns in motion,
between start and stop of any two paths that
aren't the same path yet have same start and stop.
Then it's figured quarks usually have no torque except
holding together.