Abstract
We consider the problem of integrability by quadratures of normal Hamiltonian system in sub-Riemannian problem on the groups of motions of hyperbolic plane or pseudo Euclidean plane which form the Lie group SH(2). The first step towards proof of integrability is to calculate the local representation of the Lie group SH(2) in canonical coordinates of second kind. Wei-Norman transformation is applied to obtain this local representation. The Wei-Norman representation shows that the left invariant control system defined on the Lie group SH(2) is equivalent to the motion of a unicycle on hyperbolic plane. Three integrals of motion satisfying the Liouville's integrability conditions are then calculated to prove that the normal Hamiltonian system is integrable by quadratures.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
