How Does Pendulum Motion Affect Work and Kinetic Energy Calculations?

[stateofdogma]

no nevermind, i think it works if you consider the dot product a distribution over a negative differential.

 

[haruspex]

no nevermind, i think it works if you consider the dot product a distribution over a negative differential.

Not sure what you mean by that, but to be clear, no, ds does not mean abs(ds). If the range "a to b" is such that the variable of integration, x say, decreases from 'lower' bound a to 'upper' bound b then dx is negative. E.g. $\int_a^b f.dx = -\int_b^a f.dx$.