Question

A quicker way to verify that a function is a constant of motion?

Answer 1

In mechanics, a constant of motion is a quantity that is conserved throughout the motion, imposing in effect a constraint on the motion. However, it is a mathematical constraint, the natural consequence of the equations of motion, rather than a physical constraint (which would require extra constraint forces). Common examples include specific energy, specific linear momentum, specific angular momentum and the Laplace–Runge–Lenz vector (for inverse-square force laws).

Answer 2

For the sake of accuracy, this section should be entitled "One dimensional equations of motion for constant acceleration". Given that such a title would be a stylistic nightmare, let me begin this section with the following qualification. These equations of motion are valid only when acceleration is constant and motion is constrained to a straight line.

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