Principles of Mathematical Physics
www.maths.ed.ac.uk › ~jmf › TeachingThis mathematical fact turns out to have an important physical consequence. Let x(t) be a physical trajectory for a particle in a force field for which x(0) ˘x0 is a point of equilibrium; that is, a point where the force field vanishes. Then if x˙(0) ˘0 then x(t) ˘ x0 for all t. Indeed, the constant trajectory x(t) ˘ x0 for all t obeys ...