- #1

curlofgradient

## Homework Statement

A friend and I are going through Vladimir Arnold's

*Mathematical Methods of Classical Mechanics*, but I think my lack of a background in pure math / proofs is seriously hampering my ability to do any of the problems in the first chapter. For example:

PROBLEM. Show that if a mechanical system consists of only one point, then its acceleration in an inertial coordinate system is equal to zero ("Newton's First Law").

*Hint*. By Examples 1 and 2 the acceleration vector does not depend on [itex]\textbf{x}[/itex], [itex]\textbf{v}[/itex], or [itex]t[/itex], and by Example 3 the vector [itex]\textbf{F}[/itex] is invariant with respect to rotation.

## Homework Equations

Examples 1, 2, and 3 refer to the facts that Newton's equations must be invariant with respect to galilean transformations; 1 is translation through time, 2 is translation through space and the addition of a constant velocity term, and 3 is rotations in space.

## The Attempt at a Solution

Honestly, I can't see how the hint doesn't already constitute a solution! I'm not sure what more the book wants from me. I could write down the equations for the three examples, but that seems too trivial. Any help would be appreciated, especially if someone could point me towards resources for learning how to do math-based proofs specifically in the context of physics.