Unbiased Rotational Moves for Rigid-Body Dynamics

Unbiased rotational moves for rigid-body dynamics.

We introduce an unbiased protocol for performing rotational moves in rigid-body dynamics simulations. This approach-based on the analytic solution for the rotational equations of motion for an orthogonal coordinate system at constant angular velocity-removes deficiencies that have been largely ignored in Brownian dynamics simulations, namely errors for finite rotations that result from applying...

Title : Rigid body dynamics

3D Rigid Body Dynamics

The difficulty of describing the positions of the body-fixed axis of a rotating body is approached through the use of Euler angles: spin ψ̇, nutation θ and precession φ shown below in Figure 1. In this case we surmount the difficulty of keeping track of the principal axes fixed to the body by making their orientation the unknowns in our equations of motion; then the angular velocities and angula...

Frictional Rigid Body Dynamics

Practical problems like regulating robot grippers critically rely on accurately predicted friction forces. Qualified methods are derived and discussed subsequently. Special attention is paid to the question of solution existence. A time-stepping scheme which supports Coulomb friction and inelastic impacts is implemented and the numerical results are analyzed. The approach proofs to be stable, a...

Nonuniform Fourier Transforms for Rigid-Body and Multidimensional Rotational Correlations

The task of evaluating correlations is central to computational structural biology. The rigid-body correlation problem seeks the rigid-body transformation (R, t), R ∈ SO(3), t ∈ ℝ3 that maximizes the correlation between a pair of input scalar-valued functions representing molecular structures. Exhaustive solutions to the rigid-body correlation problem take advantage of the fast Fourier transfor...