Abstract
This paper presents two semi-implicit algorithms based on splitting methodology
for rigid body rotational dynamics. The first algorithm is a variation of
partitioned Runge-Kutta (PRK) methodology that can be formulated as a splitting method. The second
algorithm is akin to a multiple time stepping scheme and is based on
modified Crouch-Grossman (MCG) methodology, which can also be expressed as
a splitting algorithm. These algorithms are second-order accurate and time-reversible;
however, they are not Poisson integrators, i.e., non-symplectic.
These algorithms conserve some of the first integrals of motion, but some others
are not conserved; however, the fluctuations in these invariants are bounded
over exponentially long time intervals. These algorithms exhibit excellent
long-term behavior because of their reversibility property and their
(approximate) Poisson structure preserving property.
The numerical results indicate that the proposed algorithms
exhibit superior performance compared to some of the
currently well known algorithms such as the Simo-Wong algorithm, Newmark algorithm,
discrete Moser-Veselov algorithm, Lewis-Simo algorithm, and the LIEMID[EA] algorithm.