a generalized coordinate of a mechanical system that does not appear in the system's Lagrangian function or other characteristic functions. The presence of ignorable coordinates simplifies the integration of the corresponding differential equations of motion of a mechanical system.

How do you find ignorable coordinates?

EXAMPLE of an ignorable coordinate, a constrained coordinate and a free coordinate: the SPHERICAL PENDULUM (with θ being the angle with the vertical such that θ=0o is straight up, θ=90o being horizontal; φ is the angle measured in the horizontal plane) : KE = ½m(r'² + r²θ'² + r²sin²θφ'²) and PE = mgrcos(θ) .

What are cyclic or ignorable coordinates?

A coordinate ' k q ' is said to be cyclic or ignorable if it is explicitly absent in the Lagrangian function L. q . Thus, the generalized momentum conjugate to a cyclic coordinate is an integral of motion.