![]() ![]() Integrated along some path to find the total work done.Ĭan someone answers those points and tell me if my conclusion is correct? So if a force varies from point to point, I could represent it as a one-form field that can be 22:44 mathematical physics - Representing forces as one-forms - Physics Stack Exchange The point, then it'll be a form that when given a vector, gives the work done moving a particle Now if i take some vector we can compute, however,Īnd hence and so my conclusion is: if I interpret force at a point as a one-form at Interpret some force at the point as some one form then we'll have Then spans the cotangent space, and so, if we ![]() I tried to give this interpretation: suppose we're dealing with some manifold and suppose In second place, if the force isn't conservative, is it correct to think of it as a one form yet ? But The force by the one-form obtained by the exterior derivative of the potential, in other words My question then is: if a force is conservative with potential then it's correct do represent That's fine, it says that force is a covector, but the point is: when we start thinking aboutĬurved spaces, in general instead of talking about gradients and covectors we talk about Interpreting Vector fields as Derivations on Which is the potential so that we can write. The point here is: if some force is conservative, then there's some scalar field This question arose because of my first question It onlyĪsked 8 years, 11 months ago Active 3 years, 11 months ago 3k timesViewed Prévia do material em texto 22:44 mathematical physics - Representing forces as one-forms - Physics Stack ExchangeĪcademics and students of physics.
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