Recent content by RazorSphinx

  1. R

    Does kinetic energy depend on position as well as velocity?

    Chris, Thanks for the quotes. Makes sense, since they are talking about coordinates and their rate of change. In that case, KE can certainly depend on ##{q}## and ##\dot{q}##. However, the way I see it, this only happens because the velocity itself depends on ##\dot{q}## and ##{q}##, either...
  2. R

    Does kinetic energy depend on position as well as velocity?

    This is confusing. Are we saying that for the same velocity, just varying position can result in different KE? I can see that KE can depend on position - but only because velocity depends on position - see AlephZero's example in post #5 I suppose it boils down to what we mean by velocity - if...
  3. R

    Understand the major arc connecting two points on a sphere

    Hi AT, Thanks for that explanation. The parameterization of the two curves using M1 and M2 really helps see the repetition along M1. I think that resolves my question. Once again thanks to Simon, AT and Orodruin. Now I can move on to page 8. of Landau Lifshitz Mechanics.
  4. R

    Understand the major arc connecting two points on a sphere

    Thanks for the proof Orodruin! After my response to AT, I went back and read some more about saddle points and it seems that by definition if you can find a smaller value and a larger value near a stationary point, it is a saddle point. So, by that definition it is a saddle point. I was stuck...
  5. R

    Understand the major arc connecting two points on a sphere

    Hi A.T. Thanks. Initially, I did think that it might be a saddle point (and it may still be). However, when I try to visualize a surface with saddle point, I run into another problem 1. Either the surface has no global minimum - which not the case in our example. OR 2. The surface has at...
  6. R

    Understand the major arc connecting two points on a sphere

    Hi Simon, Firstly, thanks for the response. Of course the greater arc is not a solution to the shortest path problem. However it is a solution to the stationary path problem. I also understand that there is no global maxima - the big scribble you mention takes care of that. My dilemma arises...
  7. R

    Understand the major arc connecting two points on a sphere

    I am not sure if this is the right forum for this question, but I arrived at the question while studying the principle of stationary action so here it is: Consider the problem of finding the shortest path between two non-antipodal points on a sphere. Usually one solves this by using calculus of...
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