On the existence of normal mode of vibrations of nonlinear systems with two degrees of freedom

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Abstract
A nonlinear, conservative system having two degrees of freedom is considered. The potential energy is subject to certain restrictions which are consistent with the strain energy of springs. Then, the notion of transversals; i.e., of curves orthogonal to equipotential lines, is introduced in order to prove the existence of an in-phase and of an out-of-phase normal mode of vibration, no matter how nonlinear the springs. It is shown, that the transversals are also very helpful in the discussion of general motions of the system.

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