कोटैंजेंट इसके अंग्रेजी अर्थ का उदाहरण

The associated graded ring gr DX is given by regular functions on the cotangent bundle T∗X.

The characteristic variety Ch(M) of any D-module M is, seen as a subvariety of the cotangent bundle T∗X of X, an involutive variety.

The differential of a function f: Rk → R can be interpreted as a section of the cotangent bundle of RK given by df: Rk → T*Rk.

While the upper bound is an immediate consequence of the above interpretation of in terms of the cotangent bundle, the lower bound is more subtle.

The realization that the phase space in classical mechanics admits a natural description as a symplectic manifold (indeed a cotangent bundle in most cases of physical interest), and symplectic topology, which can be thought of as the study of global issues of Hamiltonian mechanics, has been a fertile area of mathematics research since the 1980s.

Another classical case occurs when M is the cotangent bundle of \mathbb{R}^3 and G is the Euclidean group generated by rotations and translations.

Here "pi; is the projection of the cotangent bundle T*M to M, and "pi;* is the pullback of a vector bundle.

The associated graded algebra is the commutative algebra of smooth functions on the cotangent bundle T^*M which are polynomial along the fibers of the projection \pi\colon T^*M\rightarrow M.

This is because the fibers of the frame bundle must necessarily, by definition, connect the tangent and cotangent spaces of space-time.

United States federal banking legislation In mathematics, a coframe or coframe field on a smooth manifold M is a system of one-forms or covectors which form a basis of the cotangent bundle at every point.

Let N be a smooth manifold and let T^*N be its cotangent bundle, with projection map \pi : T^*N \rightarrow N.

The characteristic variety is defined to be the subvariety of the cotangent bundle cut out by the radical of the annihilator of gr M, where again M is equipped with a suitable filtration (with respect to the order filtration on DX).

The strongest results are obtained for over-determined systems ([system]s), and on the characteristic variety cut out by the symbols, in the good case for which it is a Lagrangian submanifold of the cotangent bundle of maximal dimension (involutive systems).