Finsler Connection for General Lagrangian Systems. Issue 2 (October 2016) - Kozma, László; Ootsuka, Takayoshi
Abstract : We give a new simplified definition of a nonlinear connection of Finsler geometry which could be applied not only for regular cases but also for singular ones. For the regular case, it corresponds to the nonlinear part of the Berwald connection, but our connection is expressed not in the line element space but in the point-Finsler space. From this point of view we recognize a Finsler metric L ( x, dx ) as a "nonlinear form", which could be regarded as a generalization of the original expression of Riemannian metric, g μ υ ( x ) d x μ d x υ . Furthermore our formulae are easy to calculate compared to the conventional methods, which encourages applications to physics. This definition can be used in the case where the Finsler metric is singular, which corresponds to gauge constrained systems in mechanics. Some nontrivial examples of constrained systems are introduced for exposition of applicability of the connection.