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I am working on a vibration problem at work and having to review my Lagrangian Dynamics books from 30 years ago. So my question is about all of the authors of these books (and internet searches) make the same comment that this assumes that acceleration is constant. They make no further statement other than for simplicity they will use the classical definition for the Kinetic energy equation.

Why would they make that comment? When i use accelerations that are a function of time (and mass being constant) i can derive the same general equation form where kinetic energy is now just a function of time.

Though this is not a stumbling point for me, i am curious why all the authors would make that side comment that kinetic energy equation assumes that the acceleration being a constant.