cepheid said:Can't you just do a coordinate transformation from polar to cartesian? How is theta defined in terms of x and y?
Degrees of freedom refers to the number of independent variables or parameters that can affect the motion of a system. In mechanics, it is used to describe the number of ways a system can move or the number of independent coordinates required to fully specify the position of a system.
In general, the more degrees of freedom a system has, the more complex it is. This is because a higher number of degrees of freedom means there are more variables or parameters that can affect the behavior of the system, making it more difficult to predict or analyze.
Constrained degrees of freedom are those that are limited by external factors or forces, such as a constraint in the form of a fixed point or a restriction on motion. Unconstrained degrees of freedom, on the other hand, are free to move without any external limitations.
The number of degrees of freedom can have a significant impact on the stability of a system. In general, a higher number of degrees of freedom makes a system less stable, as there are more variables that can lead to unpredictable or chaotic behavior.
Yes, the number of degrees of freedom in a system can change. This can happen due to external factors or forces, such as constraints being added or removed, or due to changes in the system itself, such as the addition or removal of components.