Symplectic schemes for nonautonomous Hamiltonian system
The construction of symplectic schemes for autonomous Hamiltonian system has been systematically studied. The author considers the following system of canonical equations \[ {dp_i\over dt}= -{\partial H\over\partial q_i},\quad {dq_i\over dt}= {\partial H\over\partial p_i},\quad i=1,2,\dots,n \] with Hamiltonian function \(H(p_1,\dots, p_n, q_1,\dots, q_n,t)\). Using the time \(t\) as an additional dependent variable, the author considers the extended \(2n+2\) dimensional phase space \(z= (p_1,\dots, p_n,h\), \(q_1,\dots, q_n,t)\), here \(t\) and \(h\) being merely alternative notations for \(q_{n+1}\) and \(p_{n+1}\). Note that after adding the time \(t\) to the mechanical variables, every system becomes conservative. The author generalizes the method of constructing symplectic schemes by generating function in the case of autonomous Hamiltonian system to that of nonautonomous system, using the scheme mentioned above.
scientific article; zbMATH DE number 1281427