Families of Canonical Transformations by Hamilton-Jacobi-Poincaré equation. Application to Rotational and Orbital Motion

Abstract

The Hamilton-Jacobi equation in the sense of Poincaré, i.e. formulated in the extended phase space and including regularization, is revisited building canonical transformations with the purpose of Hamiltonian reduction. We illustrate our approach dealing with orbital and attitude dynamics. Based on the use of Whittaker and Andoyer symplectic charts, for which all but one coordinates are cyclic in the Hamilton-Jacobi equation, we provide whole families of canonical transformations, among which one recognizes the familiar ones used in orbital and attitude dynamics. In addition, new canonical transformations are demonstrated.

21 pages

References in corpus (3)

• Geometric Hamilton-Jacobi Theory
• Hamiltonian dynamics on the symplectic extended phase space for autonomous and non-autonomous systems
• Bohlin-Arnold-Vassiliev's duality and conserved quantities

Cited by in corpus (6)

• Note on the analytical integration of circumterrestrial orbits
• Expanding the simple pendulum's rotation solution in action-angle variables
• Short-axis-mode rotation of a free rigid body by perturbation series
• Integration of the Euler-Poinsot Problem in New Variables
• A torsion-based solution to the hyperbolic regime of the J2-problem
• Short-axis-mode rotation in complex variables