1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Simple Ellipse Question

  1. Jun 27, 2011 #1


    User Avatar
    Science Advisor

    Can the semi - major and semi - minor axes of an ellipse be time dependent? More specifically, can you have time dependent semi - major and semi - minor axes present in the standard form of the ellipse? I have an equation of the form [tex]\frac{(\xi ^{1}(t))^{2} }{a^{2}} + \frac{(\xi ^{2}(t))^{2}}{b^{2}} = 1 [/tex] where [itex]\xi ^{\alpha }[/itex] are components of a separation vector, [itex]a^{2} = [2 + \frac{1}{2}sin^{2}\omega t](\xi ^{1}(0))^{2}[/itex], and [itex]b^{2} = [2 + \frac{1}{2}sin^{2}\omega t](\xi ^{2}(0))^{2}[/itex] but I don't know if the standard form can actually have time dependent semi - major and minor axes.
  2. jcsd
  3. Jun 28, 2011 #2


    User Avatar
    Staff Emeritus
    Science Advisor

    Yes, of course. However what you are writing does NOT.
    [tex]\frac{\xi^1(t))^2}{a^2}+ \frac{\xi^2(t))^2}{b^2}= 1[/tex]
    is a single ellipse with axes of length a and b for all t. If t is "time", this could be interpreted as an object moving around that fixed ellipse with changing speed.

    An ellipse with "time dependent sem- major and minor axes" would be
    [tex]\frac{x^2}{(a(t))^2}+ \frac{y^2}{(b(t))^2}= 1[/tex]

    You can add "time dependence" or dependence on any other variable at will, just by making some parameters function of that variable.
  4. Jun 28, 2011 #3


    User Avatar
    Science Advisor

    So if in the original equation, If I had the usual X and Y instead of the time dependent separation vector but with the same form of the semi - major and minor axes that I posted above then it would be allowed? Thanks for the reply.

    EDIT: Never mind I get what you are saying. I think I should have had the initial coordinate separations on the top and the time variance of the separation plus the sin terms on the bottom.
    Last edited: Jun 28, 2011
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: Simple Ellipse Question
  1. Question about Ellipse (Replies: 11)