Geodesics on the Momentum Phase Space with metric $^{{C}}{g}$

Abstract

In this paper, a system of the differential equations giving geodesics on the momentum phase space with pseudo Riemann metric $^{C}g$ of a Hamilton space is found by using the Euler Lagrange equations. Then, space like geodesics on pseudo hyperbolic 2-space $H_{1}^{2}$ are obtained. Finally, a system of the differential equations giving geodesics on the cotangent bundle with pseudo Riemann metric $^{C}g$ of $H_{1}^{2}$ is get.

Keywords

• the hamilton mechanic system
• geodesics on the cotangent bundle
• spacelike surface