Phase space. Phase trajectories.

In summary, the conversation discusses the use of equations and trajectories in both kinematics and dynamics. It is mentioned that in kinematics, equations of motion for x and y can be obtained by eliminating time, while in dynamics, equations for x and p can be obtained in the same way. However, it is argued that phase space can be relevant for both kinematic and dynamic problems, even if it is mostly used in the latter situation. It is also noted that phase space can be used for simple mechanical systems with only kinematic state, such as position and velocity. The question posed at the end is whether this understanding is correct.
  • #1
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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  • #2
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).
 

FAQ: Phase space. Phase trajectories.

What is phase space?

Phase space is a mathematical concept used in physics and engineering to describe the state of a dynamical system. It is a multi-dimensional space where each dimension represents a different variable that defines the system's state.

How is phase space different from physical space?

Physical space refers to the three-dimensional space that we can see and interact with. Phase space, on the other hand, is an abstract mathematical space that represents the state of a dynamical system. It may have more or fewer dimensions than physical space and is used to describe the behavior of a system over time.

What are phase trajectories?

Phase trajectories are curves that represent the evolution of a system in phase space. They show how the state of the system changes over time as it moves through different points in phase space. Each point on the trajectory corresponds to a specific state of the system at a specific time.

How are phase space and phase trajectories useful in science?

Phase space and phase trajectories are useful tools for studying the behavior of complex systems, such as physical systems, chemical reactions, or even biological systems. They allow scientists to visualize and analyze the evolution of a system over time and make predictions about its future behavior.

Can phase space and phase trajectories be applied in other fields besides physics?

Yes, phase space and phase trajectories have applications in various fields, including economics, ecology, and even social sciences. They can be used to model and analyze the behavior of systems that involve multiple variables and interactions, providing valuable insights and predictions.

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