A theorem for n-dimensional strongly non-linear dynamical systems

n-dimensional strongly non-linear dynamical systems are more difficult to s olve analytically. In this paper, a new theorem which can be used to constr uct approximate analytical solutions of these systems is presented. This th eorem extends the averaging theorem for weakly non-linear systems. It is ap plied to an example which is related to rotor dynamics. The analytical solu tions obtained are in perfect agreement with the numerical computations for large values of the coefficient of nonlinearity. The advantage of the pres ented theorem lies in its simplicity and ease of applications. (C) 2001 Els evier Science Ltd. All rights reserved.