The Michigan Mathematical Journal · 1969 · 51 citations · 0 references
Natural SciencesMathematicsPhysicsDifferential EquationsDynamical SystemsMathematical PhysicsConservative SystemsContinuous Dynamical SystemsPartial Differential EquationsPerturbation MethodsPerturbation TheoryStability TheoryConservative Dynamical SystemsConservative FormulationsDifferential Equation FormulationNewtonian MechanicsPeriodic PerturbationsPeriodic Solutions Of Differential Equations
Abstract : The main result of this paper is concerned with the differential equation (1) the second derivative of x with respect to t + grad G(x) = p(t) where p epsilon C(R,R superscript n) and is 2 pi-periodic, and G epsilon C superscript 2 (R superscript n,R). The equation (1) can be interpreted physically as the Newtonian equations of motion of a mechanical system subject to conservative internal forces and periodic external forces. Specifically it is shown that under certain conditions, equation (1) has a 2 pi periodic solution.