Classical Dynamics of Particles and Systems · Problem 2-1

Oscillations — Marion & Thornton

Physics — Mechanics · equations-of-motion-integrability

Problem

Suppose that the force acting on a particle is factorable into one of the following forms: (a)

F(x_i, t) = f(x_i)g(t)

(b)

F(\dot{x}_i, t) = f(\dot{x}_i)g(t)

(c)

F(x_i, \dot{x}_i) = f(x_i)g(\dot{x}_i)

For which cases are the equations of motion integrable?