Symplectic quaternion scheme for biophysical molecular dynamics

Symplectic quaternion scheme for biophysical molecular dynamics was studied. A rigid body Hamiltonian for the unit quaternion, the minimal nonsingular representation of rotation commonly used in molecular dynamics simulation was derived along with a reversible, symplectic, integration scheme. A theoretical analysis that gave an explicit condition for an integrator to possess a conserved quantity, an explicit expression for the conserved quantity of a symplectic integrator and an extension of the explicit functions to general systems with flat phase space was also presented.