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How to Solve Problems in Nonlinear Conservative Systems Let us consider a dynamical system in which the dissipation og energy of so slow that it may be neglected. This neglecting this slow dissipation, we assume the law of conservation of energy , namely, that the some of the kinetic energy of the’ kinetic energy and the potential energy is a constant .In others world, the system is regarded as conservative. Specifically, we consider a particle of mass m in rectilinear motion under the action of restoring force F which is a function of the displacements x only, the differential equation of motion is thus m (d^2 x)/(dt^2 )=F(x) Where we assume that F is the different equation pf the paths defined by the solution of (13.62) in the xy phase plane: dx/dt=y dy/dt=(F(x))/m Eliminating we obtain the differential equation of the paths defined by the solution of (13.62) in the xy phase plan: dy/dx=(F(x))/my Separating variables in this equation, we obtain my dy=F(x)dx. Suppose x=x_0 and y(-dx⁄d...