title: On the energy partition in oscillations and waves.
abstract: A class of generally nonlinear dynamical systems is considered, for which the Lagrangian is represented as a sum of homogeneous functions of the displacements and their derivatives. It is shown that an energy partition as a single relation follows directly from the Euler-Lagrange equation in its general form. The partition is defined solely by the homogeneity orders. If the potential energy is represented by a single homogeneous function, as well as the kinetic energy, the partition between these energies is defined uniquely. For a steady-state solitary wave, where the potential energy consists of two functions of different orders, the Derrick-Pohozaev identity is involved as an additional relation to obtain the partition. Finite discrete systems, finite continuous bodies, homogeneous and periodic-structure waveguides are considered. The general results are illustrated by examples of various types of oscillations and waves: linear and nonlinear, homogeneous and forced, steady-state and transient, periodic and non-periodic, parametric and resonant, regular and solitary.
authors: School of Mechanical Engineering , Tel Aviv University, PO Box 39040 , Ramat Aviv, 69978 Tel Aviv, Israel.
authors: Leonid I
authors: LI
authors: Slepyan
keywords: Euler–Lagrange equations; homogeneous functions; nonlinear dynamics; solitary waves; time-dependent parameters