Introduction to Classical Mechanics · Problem 4.2

Conservation of energy and momentum — Morin

Physics — Mechanics · limiting-case

Problem

Consider the equation x¨=ax\ddot{x} = ax. If a=0a = 0, then the solution to x¨=0\ddot{x} = 0 is simply x(t)=C+Dtx(t) = C + Dt. Show that in the limit a→0a \to 0, Eq. (4.2) reduces to this form. Note: a→0a \to 0 is a sloppy way of saying what we mean. What is the proper way to write this limit?

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