lie derivative造句

• Similarly is the Lie derivative along of the-valued function.
• The Lie derivative of a scalar is just the directional derivative:
• Note also that the Lie derivative commutes with the contraction.
• To understand the structure of this target system, we use the Lie derivative.
• This is the covariant Lie derivative.
• In 1931, he introduced the definition of the Lie derivative, although according to van Dantzig.
• The Lie derivative constitutes an infinite-dimensional Lie algebra representation of this Lie algebra, due to the identity
• The restriction of the Lie derivative to the space of differential forms is closely related to the exterior derivative.
• Both the Lie derivative and the exterior derivative attempt to capture the idea of a derivative in different ways.
• Naturally occurring examples of derivations are partial derivatives, Lie derivatives, the Pincherle derivative, and the algebra.
• For a quite long time, physicists had been using Lie derivatives, without reference to the work of mathematicians.
• The bracket is also used to denote the Lie derivative, or more generally the Lie bracket in any Lie algebra.
• One formulation of the theorem states that the Lie derivative of this volume form is zero along every Hamiltonian vector field.
• Now define the observation space \ mathcal { O } _ s to be the space containing all repeated Lie derivatives.
• This statement is equivalent to the more usable condition that the Lie derivative of the tensor under the vector field vanishes:
• The Lie derivative is the rate of change of a vector or tensor field along the flow of another vector field.
• The Lie derivative of any tensor along a vector field can be expressed through the covariant derivatives of that tensor and vector field.
• It follows from the definition of the Lie derivative that the volume form is preserved under the flow of a solenoidal vector field.
• Note that these Cartan's formula can also be used as a definition of the Lie derivative on the space of differential forms.
• Where \ mathcal { L } is the Lie derivative and we used the fact that ? does not transform ( by definition ).