Roman Kozlov.


Title:

High-order conservative discretizations for some cases of the rigid body motion.

Abstract:

Modified vector fields can be used to construct high-order
structure-preserving numerical integrators for
ordinary differential equations.
We consider high-order integrators based
on the implicit midpoint rule, which conserve quadratic first integrals.
It is shown that these integrators are particularly suitable
for the rigid body motion with an additional quadratic first integral.
In this case high-order integrators preserve
all four first integrals of motion.
The approach is illustrated on the Lagrange top
(a rotationally symmetric rigid body with a fixed point on the symmetry axis).
The equations of motion are considered in the
space fixed frame because in this frame
Lagrange top admits a neat description.
The Lagrange top motion includes the spherical pendulum and
the planar pendulum, which swings in a vertical plane,
as particular cases.