canonical transformation การใช้

• The interpretation of the matrices as generators of canonical transformations is due to Paul Dirac.
• Linear canonical transformations are the linear transforms of the time frequency representation that preserve the symplectic form.
• In classical mechanics, a canonical transformation of phase space coordinates is one which preserves the structure of the Poisson brackets.
• Check out the articles canonical transformation and symplectomorphism .  talk ) 14 : 52, 27 July 2012 ( UTC)
• The change of variable between one set of canonical coordinates and another is a "'canonical transformation " '.
• Very relevant contributions to this approach are due to his German colleague Carl Gustav Jacobi [ 1804 1851 ] in particular referring to canonical transformations.
• Named after the physicist and mathematician flow of a Hamiltonian vector field are known as canonical transformations in physics and ( Hamiltonian ) symplectomorphisms in mathematics.
• Canonical transformations that do not include the time explicitly are called "'restricted canonical transformations "'( many textbooks consider only this type ).
• Canonical transformations that do not include the time explicitly are called "'restricted canonical transformations "'( many textbooks consider only this type ).
• I don't dispute that only some special types of transformations ( like canonical transformations ) preserve the equations of motion despite changing the Lagrangian and Hamiltonian.
• Canonical coordinates can be obtained from the generalized coordinates of the Lagrangian formalism by a Legendre transformation, or from another set of canonical coordinates by a canonical transformation.
• Time evolution is a canonical transformation, since the phase space at any time is just as good a choice of variables as the phase space at any other time.
• As described below, this equation may be derived from Hamiltonian mechanics by treating " S " as the generating function for a canonical transformation of the classical Hamiltonian
• The FRFT can be used to define fractional convolution, correlation, and other operations, and can also be further generalized into the linear canonical transformation ( LCT ).
• For example, he developed a theory of canonical transformations which allowed changing coordinates so that some coordinates disappeared from the Lagrangian, as above, resulting in conserved canonical momenta.
• The elements of the group are, in a certain sense, canonical transformations on this vector, i . e . they preserve the form of Hamilton's equations.
• However, the class of canonical transformations is much broader, since the old generalized coordinates, momenta and even time may be combined to form the new generalized coordinates and momenta.
• A change of coordinates that preserves this form is a canonical transformation; these are a special case of a symplectomorphism, which are essentially a change of coordinates on a symplectic manifold.
• Are the generalized forces ( script Q instead of ordinary Q is used here to prevent conflict with canonical transformations below ) and "'q "'are the generalized coordinates.
• This expression is better than the others when the process leads to a known Fourier transform, and the connection with the Fourier transform is tightened in the linear canonical transformation, discussed below.