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Authors: L. Kharevych, Weiwei Y. Tong, E. Kanso, J. E. Marsden,
P. Schröder, and M. Desbrun
Abstract:
We present a general-purpose numerical scheme for time integration of Lagrangian
dynamical systems---an important computational tool at the core of
physics-based animation. Several features make this particular time integrator
highly desirable for computer animation. First, it guarantees preservation
of important invariants, such as linear and angular momenta. The symplectic
nature of the integrator also guarantees a correct energy behavior, even when
dissipation and external forces are added. Constraints can also be enforced
quite elegantly. Finally, higher-order accurate schemes can easily be derived
if needed. Two key properties set the method apart from earlier approaches.
First, the nonlinear equations that must be solved for updates are replaced by
a minimization of a novel energy-like function. Second, the formulation introduces
additional variables that provide key flexibility in the implementation of
the method. These properties are achieved using a discrete form of a general
variational principle called the Pontryagin--Hamilton principle. We show its
application to a simulation in non-linear elasticity with implementation details.
Contact
Jerry Marsden,
for more information.
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Jerry Marsden
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