Phase space. Phase trajectories.

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SUMMARY

The discussion centers on the concept of phase space and phase trajectories in both kinematics and dynamics. It establishes that phase space is applicable to both kinematic equations, such as ##x=x(t)## and ##y=y(t)##, and dynamic equations, like ##x=x(t)## and ##p=p(t)##. The elimination of time in these equations leads to the formulation of phase trajectories, demonstrating that phase space is relevant for mechanical systems with only kinematic states, including position and velocity.

PREREQUISITES
  • Understanding of kinematic equations and their representations.
  • Familiarity with dynamic equations and momentum concepts.
  • Knowledge of phase space theory in physics.
  • Basic grasp of mechanical systems and their states.
NEXT STEPS
  • Study the mathematical formulation of phase space in classical mechanics.
  • Explore the relationship between kinematics and dynamics in mechanical systems.
  • Learn about phase trajectories and their applications in physics.
  • Investigate the implications of phase space in advanced topics like Hamiltonian mechanics.
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Students of physics, mechanical engineers, and researchers interested in the applications of phase space in both kinematics and dynamics.

LagrangeEuler
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If I understand well like in kinematics where we could have eq of motion ##x=x(t)##, ##y=y(t)## and we get eq of trajectory with elimination of time. In dynamics we have ##x=x(t)##, ##p=p(t)## and with elimination of time we get eq of phase trajectory. Am I right?
 
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If I read your question correct, no. I see no reason why phase space can't be just as relevant for both for a purely kinematic set of equations as for a dynamical problem, even if we mostly use the term phase space in the later situation. For instance, phase space makes perfect sense also for simple mechanical systems which has only kinematic state (like position and velocity).
 

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