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!

Homework Help: How to get transfer function (freq. domain) from Newton's 2nd Law Eqn

  1. Apr 15, 2014 #1
    1. The problem statement, all variables and given/known data

    I am given the following dynamic system. I want to find the transfer function, θ1(s)/T(s).

    The main body of the satellite, J1, acts like a large mass flying through space; space is essentially without friction and therefore no damping is imparted on the main body. The solar collector array acts like a second order underdamped system attached to the satellite, adding second order underdamped modes to the system. The satellite has thrusters that can impart a torque T(t) on the satellite main body; attitude θ1(t) can be measured; gravity from nearby planets is negligible about the axis of rotation; the structure attaching the main body to the solar collector acts as a torsional spring k and torsional damper b.

    T(s) is the plant input, and θ1(s) is the plant output.


    2. Relevant equations

    Newton's 2nd Law (F=ma)

    Laplace Transform?

    3. The attempt at a solution

    I came up with the following two equations (which I believe describe each body in the above dynamic system):

    J1*θ1''(t) = -b*[θ1'(t) - θ2'(t)] - k*[θ1(t) - θ2(t)] + T(t)

    J2*θ2''(t) = -b*[θ2'(t) - θ1'(t)] - k*[θ2(t) - θ1(t)]

    As you can see, these are in the time domain (where θ''(t) = a(t), the second derivative of position; θ'(t) = v(t), the first derivative of position). I am unsure how to now get the transfer function from these equations (and in turn get these into the frequency domain). The transfer function is θ1(s)/T(s).

    Should I take the Laplace Transform of the two equations? I am sure there is something else I am missing. Any light shed on this is GREATLY appreciated! Have a nice day :)
  2. jcsd
  3. Apr 16, 2014 #2


    User Avatar
    Gold Member

    Taking the laplace transform of the two equations is a good place to start
  4. Apr 16, 2014 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

    And the problem statement is ... ?
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted