Physics Notes - Herong's Tutorial Notes
∟Poisson Bracket Expression
This chapter provides an introduction of phase space and phase portrait. Topics include Poisson Bracket as a partial differential expression; Hamilton Equations in Poisson Brackets; total time derivative of observables.
What Is Poisson Bracket
Poisson Bracket and Hamilton Equations
Observables in Phase Space
Poisson Bracket in Portrait Space Transformation
Takeaways:
- Poisson Bracket {f, g} is a partial differential expression of two functions f and g on the phase space.
- Poisson Bracket {f, g} is the dot product of gradient vector of f
and the symplectic gradient vector of g.
- Hamilton Equations in terms of Poisson Brackets are: p' = {p, H} and q' = {q, H}.
- Total time derivative of any observable, f, can be expressed as:
df/dt = ∂f/∂t + {f, H}.
- Poisson Bracket is invariant under a portrait space transformation:
{f, g}Q,P = {f, g}q,p.
Table of Contents
About This Book
Introduction of Space
Introduction of Frame of Reference
Introduction of Time
Introduction of Speed
Newton's Laws of Motion
Introduction of Special Relativity
Time Dilation in Special Relativity
Length Contraction in Special Relativity
The Relativity of Simultaneity
Introduction of Spacetime
Minkowski Spacetime and Diagrams
Introduction of Hamiltonian
Introduction of Lagrangian
Introduction of Generalized Coordinates
Phase Space and Phase Portrait
►Poisson Bracket Expression
References
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