Complete Integrability for Lagrangian Dependent on Acceleration in a Space-Time of Constant Curvature

Abstract

The equations of motion for a Lagrangian $\mathcal{L}(k_1)$, depending on the curvature $k_1$ of the particle worldline, embedded in a space--time of constant curvature, are considered and reformulated in terms of the principal curvatures. It is shown that for arbitrary Lagrangian function $\mathcal{L}(k_1)$ the general solution of the motion equations can be obtained by integrals. By analogy with the flat space--time case, the constants of integration are interpreted as the particle mass and its spin. As examples, we completely investigate Lagrangians linear and quadratic in $(k_1)$ and the model of relativistic particle with maximal proper acceleration, in a space--time with constant curvature.

18 pages, LATEX

References in corpus (4)

• Dynamics of relativistic particle with Lagrangian dependent on acceleration
• Spin and Electron Structure
• Electron structure, Zitterbewegung, and the new non-linear Dirac-like equation
• On squaring the primary constraints in a generalized Hamiltonian dynamics

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