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Math Help - Path of an orbiting object

  1. #1
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    Path of an orbiting object

    I am a clueless math noob, and I hope the overlords of the internet can help me explain, what I cannot.

    Hopefully someone can explain, not only the formula itself, but also learn me how I can understand it.

    The problem is as follows:

    I want to describe the orbit of an object in a formula.
    The object travels in a circular path, but is controlled by an arm, set off-center from the center of its path.

    The arm rotates in a constant speed.

    So my problem is, how can I describe this mathematically?


    Thanks for reading my post
    Attached Thumbnails Attached Thumbnails Path of an orbiting object-simplemspaintsketch.png  
    Last edited by Stig; August 31st 2012 at 08:15 AM. Reason: I cant' spell
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  2. #2
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    Re: Path of an orbiting object

    Quote Originally Posted by Stig View Post
    I am a clueless math noob, and I hope the overlords of the internet can help me explain, what I cannot.

    Hopefully someone can explain, not only the formula itself, but also learn my how I can understand it.

    The problem is as follows:

    I want to describe the orbit of an object in a formula.
    The object travels in a circular path, but is controlled by an arm, set off-center from the center of its path.

    The arm rotates in a constant speed.

    So my problem is, how can I describe this in mathematically?


    Thanks for reading my post
    If I understand your question correctly this is only possible if the length of the arm is variable.

    1. The orbit is a circle with radius R (= constant). The center of rotation is in a distance d from the center of the orbit. (see attachment)

    2. From the Cosine rule you know:

    R^2=d^2+r^2-2dr \cdot cos(\theta)

    This ia a quadratic equation in r. Solve for r. I've got:

    r = d \cdot \cos(\theta) \pm \sqrt{d^2 \cdot (\cos(\theta))^2 + R^2 - d^2}

    3. Use this equation together with a polar coordinate system.

    4. For instance with R = 4, d = 2 you'll get a circle around (2, 0) radius 4 and the center of rotation (of the "arm") is the origin.
    Attached Thumbnails Attached Thumbnails Path of an orbiting object-circorbit.png  
    Thanks from Stig
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  3. #3
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    Re: Path of an orbiting object

    Thank you so very much!
    I owe you a beer
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  4. #4
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    Re: Path of an orbiting object

    I have another issue which I hope can be explained...
    If the object has a mass, how will the forces be distributed?
    Say if one kg moves at the circular path, how much outward force will be distributed in this circle?
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