Sentence examples for manifold is defined from inspiring English sources

For the former, a sliding manifold is defined by combining the position and velocity tracking errors of one state variable, i.e., the sliding manifold has two coefficients.

This manifold is defined based on the specified geometric relations among the generalized coordinates of the system which are called virtual holonomic constraints.

The geometry of this manifold is defined based on specified geometric relations among the generalized coordinates of the system which are called virtual holonomic constraints.

However, the rotation matrices are approximated by using a single Gauss Newton step with a fixed updating step length, which can lead to a considerable performance drop in the rotation reconstruction if no proper metric on the manifold is defined.

This manifold is defined by the the path that links a saddle with an attractor point.

The order parameter and space-time manifold are defined as t ∈ T and ( q 1, …, q n ) ∈ M, respectively.

We also give a non-commutative generalization of the well-known fact that the integral curves of a vector field on a compact manifold are defined on all of R.

The 2PBVPs of the three submanifolds that constitute the computed saddle slow manifold are defined by Eq. (6) with boundary conditions (9), (10) as specified by (16), and one of (17), (18) or (19).

The study of algebraic geometry was amenable to the topological methods of Poincaré and Lefschetz so long as the manifolds were defined by equations whose coefficients were complex numbers.

Warped product manifolds were defined and studied by Bishop and ONeill [5] as a natural generalization of the Riemannian product manifolds.

Finally, Grassmann distance between manifold subspaces is defined as a damage index.