Motion - WikiMechanics

Motion

Sir Isaac Newton. Painted by G Kneller 1689.

Momentum is the principal descriptor of motion. Indeed momentum is literally the modern English word used for translating the phrase "quantity of motion" that Newton uses¹ on the very first page of his great work, the Principia. So to understand motion we start by defining momentum; consider a particle P characterized by some repetitive chain of events

$\mbox{\fontsize{14}{18}\selectfont $ \Psi ^{\sf{P}} = \left( \sf{\Omega}_{0} , \sf{\Omega}_{1} \ \ldots \ \sf{\Omega}_{\it{j}} \ \ldots \ \right) $}$

where each orbital cycle is a bundle of N quarks

$\mbox{\fontsize{14}{18}\selectfont $ \sf{\Omega} = \left\{ \sf{q}_{1}, \sf{q}_{2}, \ \ldots \ \sf{q}_{\it{i}} \ \ldots \ \sf{q}_{\it{N}} \right\} $}$

Let each quark be described by its inertia I. And report on any changes relative to a frame of reference F which is characterized using Ĩ the average inertia of a quark in F. Phase relationships are noted by ϵ. And the number c is a constant. Definition: the momentum of quark q in reference frame F is the ordered set of three numbers

$\mbox{\fontsize{14}{18}\selectfont $ \overline{p}^{\,\sf{q}} \equiv \left( \ \epsilon^{\sf{q}} \overline{I}^{\,\sf{q}} - \widetilde{I}^{\,\sf{F}} \ \right) /c $}$

and the momentum of particle P in the F-frame is defined by a sum over the quarks in P

$\mbox{\fontsize{14}{18}\selectfont $ \overline{p}^{\,\sf{P}} \equiv \sum _{ \it{i} = 1 } ^{\it{N}} \ \overline{p} ^{\, \sf{q}} _{\it{i}} $}$

Inertia is conserved when compound quarks are formed

$\mbox{\fontsize{14}{18}\selectfont $ \overline{I}^{\,\sf{P}} = \sum _{ \it{i} = 1 } ^{\it{N}} \ \overline{I} ^{\, \sf{q}} _{\it{i}} $}$

so if P is a monophase particle then its momentum is given by

$\mbox{\fontsize{14}{18}\selectfont $ c \overline{p} = \epsilon \overline{I}^{\,\sf{P}} - N \widetilde{I}^{\,\sf{F}} $}$

The norm of the momentum is marked by

$\mbox{\fontsize{14}{18}\selectfont $ p \equiv \left\| \, \overline{p} \, \right\| $}$

Definitions: if p = 0 we say that P is stationary or at rest in the F-frame. Or if p ≠ 0 we say that P is in motion. The direction of motion is the ordered set of three numbers

(1)

$\mbox{\fontsize{12}{14}\selectfont $ \hat{p} \equiv $} \fontsize{12}{14} \begin{cases} (0,0,0) &\text{ \sf{if} $p = 0$ } \ \ \overline{p}/p &\text{ \sf{if} $p \ne 0$ } \end{cases}$

Sensory Interpretation: the momentum is defined by a difference between the inertias of P and F. Recall that inertia has previously been interpreted as a mathematical representation of visual sensation. So momentum can be understood as the visual contrast between P and F. If P is at rest in the F frame, then the proportions of their visible sensations are the same as each other.

Next step: conservation of momentum.

Page tags: direction momentum motion newton rest stationary

page_revision: 489, last_edited: 1283460459|%e %b %Y, %H:%M %Z (%O ago)

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