Lesson plan
Generalized coordinates
In analytical mechanics, generalized coordinates are a set of parameters used to represent the configuration of a system in a configuration space. These parameters must uniquely define the configuration of the system relative to a reference configuration. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized" distinguishes these parameters from the traditional use of the term "coordinate" to refer to Cartesian coordinates. An example of a generalized coordinate would be to describe the position of a pendulum using the angle of the pendulum relative to vertical, rather than by the x and y position of the pendulum. Although there may be many possible choices for generalized coordinates for a physical system, they are generally selected to simplify calculations, such as the solution of the equations of motion for the system. If the coordinates are independent of one another, the number of independent generalized coordinates is defined by the number of degrees of freedom of the system. Generalized coordinates are paired with generalized momenta to provide canonical coordinates on phase space.
Article summary
In analytical mechanics, generalized coordinates are a set of parameters used to represent the configuration of a system in a configuration space. These parameters must uniquely define the configuration of the system relative to a reference configuration. The generalized velocities are the time derivatives of the generalized coordinates of the system. The adjective "generalized" distinguishes these parameters from the traditional use of the term "coordinate" to refer to Cartesian coordinates. An example of a generalized coordinate would be to describe the position of a pendulum using the angle of the pendulum relative to vertical, rather than by the x and y position of the pendulum. Although there may be many possible choices for generalized coordinates for a physical system, they are generally selected to simplify calculations, such as the solution of the equations of motion for the system. If the coordinates are independent of one another, the number of independent generalized coordinates is defined by the number of degrees of freedom of the system. Generalized coordinates are paired with generalized momenta to provide canonical coordinates on phase space.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.