What is the Difference Between Phase Trajectory and Trajectory in Robotics?

[supernova1387]

I was reading an article about robotics stuff and I came across with this word "phase trajectory". I know what the phase plot is but what are trajectory and phase trajectory and is there any difference between them?

Regards

 

[Gokul43201]

In general terms, the state of a classical system can be described by a point in the appropriate phase space. For instance, for a system of N particles, the positions and (conjugate) momenta of each of the particles provides a description of the system.

The vector \left( x_1, x_2, ..., x_N, y_1, y_2, ..., y_N, z_1, z_2, ..., z_N, p_{x1}, p_{x2}, ...p_{xN}, p_{y1}, p_{y2}, ..., p_{yN}, p_{z1}, p_{z2}, ..., p_{zN} \right) is a point in a 6N-dimensional space that identifies the state of this system at some instant of time. As the system evolves over time, it is described by a different point in phase space at each different instant of time. A phase trajectory is simply the path through phase space traced out by the state vector as it passes through these points at different times.

 

[supernova1387]

In general terms, the state of a classical system can be described by a point in the appropriate phase space. For instance, for a system of N particles, the positions and (conjugate) momenta of each of the particles provides a description of the system.

The vector \left( x_1, x_2, ..., x_N, y_1, y_2, ..., y_N, z_1, z_2, ..., z_N, p_{x1}, p_{x2}, ...p_{xN}, p_{y1}, p_{y2}, ..., p_{yN}, p_{z1}, p_{z2}, ..., p_{zN} \right) is a point in a 6N-dimensional space that identifies the state of this system at some instant of time. As the system evolves over time, it is described by a different point in phase space at each different instant of time. A phase trajectory is simply the path through phase space traced out by the state vector as it passes through these points at different times.

Thank you very much for clear explanation.

 

[Landau]

See The Encyclopaedia of Mathematics.

 

[HallsofIvy]

A "phase trajectory", which is the same as just "trajectory" as long as it is understood that we are talking about a phase diagram, is a curve in the phase diagram that is at all points parallel to the phase vectors. And that means that it is a particular solution to the differential equation the phase diagram is based on.