On the rheonomic Finslerian mechanical systems

Abstract: In this paper it will be studied the dynamical system of a rheonomic Finslerian mechanical system, whose evolution curves are given, on the phase space TMxR, by Lagrange equations. Then one can associate to the considered mechanical system a vector field S on TMxR, which is called the canonical semispray. All geometric objects of the rheonomic Finslerian mechanical system one can be derived from S. So we have the fundamental notion as the nonlinear connection N, the metrical N-linear connection, etc.

Keywords: Rheonomic Finsler space, mechanical system, semispray, non-linear connection

Classification (MSC2000): 53C60; 53C80

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