Phase Space and Phase Portrait
This chapter provides an introduction of phase space and phase portrait. Topics include introduction of canonical coordinates of a system; trajectory curves of a system for a given period of time; phase portraits of free fall, simple harmonic, and pendulum motions; motion equations of linear systems; 2-D homogeneous linear systems.
What Is Phase Space
What Is Phase Portrait
Phase Portrait of Simple Harmonic Motion
Phase Portrait of Pendulum Motion
Motion Equations of Linear Systems
Phase Portraits of 2-D Homogeneous Linear Systems
- Phase Space is the collection of all possible sets of canonical coordinates
of a system.
- Canonical Coordinates are generalized position components, qi,
extended with generalized momentum components pi.
- Phase Portrait is the trajectory curve of
a system in the the Phase Space for a given period of time.
- Motion equations in a linear system are
first order linear differential equations of the canonical coordinates.
- 2-D homogeneous linear systems
can be classified based on characteristic polynomials of their coefficient matrixes.
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
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