# generalized momentum

## generalized momentum

[′jen·rə‚līzd mə′ment·əm] (mechanics)

Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

Link to this page:

https://encyclopedia2.thefreedictionary.com/generalized+momentum

our app

- Dictionary
- Thesaurus
- Medical

Dictionary - Legal

Dictionary - Financial

Dictionary - Acronyms
- Idioms
- Encyclopedia
- Wikipedia

Encyclopedia

(mechanics)

Want to thank TFD for its existence? Tell a friend about us, add a link to this page, or visit the webmaster's page for free fun content.

Link to this page:

Then we find the Hamiltonian in its two forms, with the help of 4-velocity and the generalized momentum, and substitute the Hamiltonian into Hamilton equations to verify the motion equations.

mu]]) we shall introduce the 3-vector of generalized momentum with the following components:

According to (19) for continuously distributed matter the rate of change of the generalized momentum of substance and the field is determined by gradients from the following quantities: the energy of the substance unit in gravitational and electromagnetic fields that can be found through the velocity V and the scalar and vector potentials; the integral by volume of the term with scalar spacetime curvature; the integral by volume of energy invariants of the gravitational and electromagnetic fields, which are in the volume of the substance unit, as well as those of their proper fields, which are generated by this substance and interact with it.

z] are the components of the 3-vector of the so-called conjugate generalized momentum P = ([P.

We shall find the components of the generalized momentum from (30), given that the velocity components [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] are directly included in the Lagrangian (4) according to (12) and (13) only in three terms, forming part of the Lagrangian L'.

The scalar product of the generalized momentum P and the velocity V, taking into account the relation [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], gives:

THE EXPRESSION OF THE HAMILTONIAN THROUGH THE GENERALIZED MOMENTUM

We express the component x of the 3-velocity through components of the generalized momentum P=([P.

z], the Hamiltonian will be expressed through the 3-vector of the generalized momentum P, through the scalar potentials [psi], [phi], and vector potentials D, A:

Hamilton's equations according to (30) and (31), with the components of 3-vector coordinate velocity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and the components of 3-vector of the generalized momentum P = ([P.

The physical meaning of equation (59) lies in the fact that the gradient of the Hamiltonian as the energy of the system, taken with opposite sign, is equal to the rate of change of the generalized momentum with time.

It is represented, though, by the physical quantities related with the interactions in which the material particle participates, by the potential energy or the generalized momentum of the material particle.

- ▲
- general supplies
- general term
- General Theory of Relativity
- general topology
- general transcription factor
- General Union of Workers
- general utility airport
- General Zod
- Generalic, Ivan
- General-in-Chief
- Generalissimo
- Generalization
- generalized anxiety disorder
- generalized binomial trials model
- Generalized Coordinates
- generalized Euclidean space
- generalized feasible flow
- generalized force
- Generalized Forces
- generalized function
- Generalized Functions
- generalized hydrostatic equation
- generalized max-flow min-cut theorem
- generalized mean-value theorem
- Generalized Momenta
- generalized momentum
- generalized other
- generalized permutation
- generalized Poincaré conjecture
- generalized power
- generalized program
- generalized ratio test
- generalized routine
- generalized s-t cut
- generalized s-t network
- generalized system
- generalized transmission function
- generalized velocity
- generally accepted standard
- Generalov, Fedor
- Generalov, Fedor Stepanovich
- Generalov, Vasilii
- Generalov, Vasilii Denisovich
- general-purpose automatic test system
- general-purpose bomb
- general-purpose computer
- general-purpose controller
- general-purpose function generator
- General-purpose Hall for Entertaining and Sports
- general-purpose language
- general-purpose systems simulation
- ▼

- ▲
- Generalized Markup Language
- Generalized Master Equation
- Generalized Matched Filter
- generalized max-flow min-cut theorem
- Generalized Maximum Likelihood Sequence Detection and Estimation
- Generalized Maximum Likelihood Sequence Estimation
- Generalized Maximum-Likelihood Estimator
- Generalized Mean Value
- generalized mean-spherical-approximation
- generalized mean-value theorem
- Generalized Memory Polynomial for Linear Crosstalk
- Generalized Memory Polynomial for Non-Linear Crosstalk
- Generalized Mersenne Number
- Generalized Method of Cells
- Generalized Method of Cells
- Generalized method of moments
- Generalized Minimal Residual Algorithm
- Generalized Minimum Distance
- Generalized Minimum Distance Decoding
- Generalized Minimum Distance Encoding
- Generalized Minimum Residual
- Generalized Minimum Spanning Tree Problem
- Generalized Minimum Variance
- Generalized Minimum Variance Decision Feedback Power Control
- Generalized Minimum Variance Incremental Power Control
- Generalized Minimum Variance Power Control
- Generalized Mode-Matching Method
- Generalized Moeller-Plesset Second-Order
- Generalized Molecular Orbital
- Generalized Momenta
- generalized momentum
- Generalized Monitoring Facility
- generalized morphea
- generalized morphea
- Generalized Multi Protocol Label Switching
- Generalized Multi-Carrier
- Generalized Multi-Carrier Code Division Multiple Access
- Generalized Multi-Code
- Generalized Multi-Modulus Algorithm
- Generalized Multi-Pole Technique
- Generalized Multi-Protocol Label Switching
- Generalized Multichannel Quantum Defect Theory
- Generalized Multiple Attractor Cellular Automata
- Generalized Multiple-Choice Knapsack Problem
- Generalized Multiresolution Analysis
- Generalized Music Plugin Interface
- Generalized Mutual Information
- generalized myokymia
- Generalized Myositis Ossificans
- Generalized Nadeau-Taylor model
- Generalized Nash Equilibrium Problem
- generalized neurodermatitis
- generalized neurodermatitis
- generalized neurodermatitis
- generalized neuropathy
- generalized neuropathy
- generalized neuropathy
- Generalized Newton Variational Principle
- Generalized Non-Adjacent Form
- Generalized Non-Convulsive Epilepsy
- Generalized Non-Data-Aided Recursive Least Squares
- ▼