canonical coordinates sentence in Hindi
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- Define relations between the new generalized coordinates and the old canonical coordinates.
- Define relations between the new generalized momenta and the old canonical coordinates.
- Here is a canonical coordinate ( or ) and ( possibly ) the time.
- The Sommerfeld quantization can be performed in different canonical coordinates and sometimes gives different answers.
- These are the metric canonical coordinates.
- See canonical coordinates for more background.
- Since the evolution of q depends upon four initial parameters, this means that there are four canonical coordinates.
- A " canonical coordinate system " consists of canonical position and momentum variables that satisfy canonical Poisson-bracket relations,
- Ideally, one can invert these relations to obtain formulae for each as a function of the old canonical coordinates.
- The change of variable between one set of canonical coordinates and another is a "'canonical transformation " '.
- The classical field is treated as a dynamical variable called the canonical coordinate, and its time-derivative is the canonical momentum.
- Non-degeneracy of L means that the canonical coordinates can be expressed in terms of the derivatives of { q } and vice versa.
- A typical example of canonical coordinates is for q _ i to be the usual Cartesian coordinates, and p _ i to be the components of momentum.
- As will be shown below, the generating function will define a transformation from old to new canonical coordinates, and any such transformation is guaranteed to be canonical.
- 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.
- 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.
- The Poisson bracket of two canonically conjugate quantities like " x " and " p " is equal to 1 in any canonical coordinate system.
- Its value does not vary with the continuous canonical coordinates, so overcounting can be corrected simply by integrating over the full range of canonical coordinates, then dividing the result by the overcounting factor.
- Its value does not vary with the continuous canonical coordinates, so overcounting can be corrected simply by integrating over the full range of canonical coordinates, then dividing the result by the overcounting factor.
- This is Ostrogradsky's instability, and it stems from the fact that the Lagrangian depends on fewer coordinates than there are canonical coordinates ( which correspond to the initial parameters needed to specify the problem ).
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