Hamiltonian systems symplectic geometry algorithms

Author: Feng Kang
Publisher:
Publish Date: 2003-12-01
Features: The foundation of Hamiltonian systems is symplectic geometry. Hamilton introduced generalized coordinates and generalized momenta to represent the energy of a system while studying Newtonian mechanics, which are now commonly referred to as the Hamiltonian function. For a system with n degrees of freedom, n generalized coordinates and n generalized momenta span a 2n-dimensional phase space. The emerging symplectic geometry can be traced back to the establishment of the KAM theorem. Hamiltonian systems are an important type of dynamical system, as all real, dissipative, and negligible physical processes can be represented as Hamiltonian systems, with a wide range of applications. Feng Kang pioneered a new branch in the field of computational methods—symplectic geometry algorithms.