Geometric Mechanics and Its Applications

Tomake the content of the book more systematic, this book mainly briefs some related basic knowledgereported by other monographs and papers about geometric mechanics. The main content of this book is based on the last 20 years' jobs of the authors. All physical processes can be formulated as theHamiltonian form with the energy conservation law as well as the symplecticstructure if all dissipative effects are ignored. On the one hand, the importantstatus of the Hamiltonian mechanics is emphasized. On the other hand, a higherrequirement is proposed for the numerical analysis on the Hamiltonian system,namely the results of the numerical analysis on the Hamiltonian system shouldreproduce the geometric properties of which, including the first integral, thesymplectic structure as well as the energy conservation law.