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Momentum is a covector?

  1. Apr 25, 2008 #1
    So this question has been asked elsewhere, yet I haven't found a clear explanation.

    Definition. momentum := mass * velocity, or
    p=m*v

    Now if we know p, then we know the direction v points in, and we get a function from R to R, which maps the magnitude of v to the mass, inverse proportionally. This seems like the only way of interpreting momentum, given the definition above.

    In order for momentum to be a covector, two independent vectors would need to evaluate to the same real value, provided they're both in the same level set (codimension 1 plane). What does this say about momentum? Can a bullet headed North have the same momentum as a bullet heading East?

    Rather, i suppose the answer is, given a bullet headed north, we can ask "what is the momentum in the direction NE?"

    Ah, now it makes sense to use a dot product, then to clean things up by considering momentum a covector. The above definition is misleading, then, we should say momentum of q _in_the_direction_v_ is defined as <mq',v>, whereby <mq'|.> is the momentum covector.

    Great!

    Andrew Marshall
     
    Last edited: Apr 25, 2008
  2. jcsd
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