Similar Motion of Two-Degree-of-Freedom Nonlinear Vibrating Systems with Nonsymmetric Springs

If similar motion occurs, it is demonstrated by a straight line (linear trajectory) in the configuration space whose orthogonal coordinates are the displacements of the masses in the vibrating system. Since the systems considered are conservative, all solutions of the equations of motion must satisfy the Principle of Least Action and its Euler-Lagrange equation. The solution of this equation defines a trajectory in configuration space, thus reducing the problem to one of geometry.