Do Generalized Coordinates Depend on Each Other?

Do Generalized Coordinates Depend on Each Other?

They are all independent of one other, and each is a function of time. Geometrically they can be lengths along straight lines, or arc lengths along curves, or angles; not necessarily Cartesian coordinates or other standard orthogonal coordinates.

What is the advantage of using generalized coordinates?

The major advantage of using generalized coordinates is that they can be chosen to be perpendicular to a corresponding constraint force, and therefore that specific constraint force does no work for motion along that generalized coordinate.

How many generalized coordinates in simple pendulum which describe the motion?

There are two generalized coordinates u and θ to define complete motion of the system.

Maya Lin-Takahashi
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Maya Lin-Takahashi

Maya is a hardware enthusiast who tests and reviews smart home devices, smartphones, wearables, and audio gear. She focuses on practical consumer value and build quality.