Sentence examples for momentum variable from inspiring English sources

Aubry-Mather theory is focused on a special family of invariant measures of Hamiltonian dynamics, for Hamiltonians which are convex in the momentum variable.

We first use the ordered over-relaxation method to draw the momentum variable which could suppress the random walk behavior in Gibbs sampling stage.

For the discretisation with respect to the momentum variable, we employ spectrally convergent basis approximations using both Legendre polynomials and Gaussian radial basis functions.

This paper presents an ordered over-relaxation Langevin Monte Carlo sampling (ORLMC) based tracking method within the Bayesian filtering framework, in which the traditional object state variable is augmented with an auxiliary momentum variable.

Letting here p k = ∂ L ∂ q k ˙ ( q, q ˙ ), k = 1, 2 …, n. be the momentum variable, and using the transformation ( q, q ˙ ) = ( q, p ) we can write (13) as the Hamiltonian, H ( p, q, t ) = ∑ j = 1 n p j q ˙ j − L ( q, q ˙ ( q, p, t ), t ).

Here, y = u − α 2 u x x is a momentum variable, the constants α 2 and γ c 0 are squares of length scales, and c 0 = g h > 0 (where c 0 = 2 ω ) is the linear wave speed for undisturbed water at rest at spatial infinity, where h is the mean fluid depth and g is the gravitational constant.

The momentum variables are expressed in separable (polar) coordinates facilitating the use of products of univariate basis expansions.

It is the energy E that we have encountered above, but expressed not in terms of position and velocity variables but rather in terms of position and momentum variables.

Using a coordinate transformation on the momentum variables, we split the kinetic energy of the system in a desired and an undesired part, and then design an (intrinsically passive) controller as an interconnection of port- Hamiltonian subsystems, in such a way that asymptotic convergence to the desired curve is obtained.

This failure is remedied by taking equally sized cells in position and momentum variables.

But the choice to take all cells equal in size in position and momentum variables is not quite self-evident, as Boltzmann himself shows.