The way to think about this intuitively is to think about your "knowns" in the equation, and how to solve for your "unknown". Your "knowns" are the following: 1)You have chess pieces set at initial positions, 2)You know where you want these chess pieces to go (final positions), and 3)you can get info on the materials involved as they can act as "dampers", and dampers affect the vibrations. Your "unknown" is the forced vibration input (i.e. how fast each motor spins at a given time). For those of you with a calculus background, you can see that this is a second order linear equation with constant coefficients ( g(t)=ay''+by'+cy ). Thus you can set up matrices using Mathcad, etc. to crunch the math...solving for the motor inputs for each unit of time.
Slashdot Mirror
The way to think about this intuitively is to think about your "knowns" in the equation, and how to solve for your "unknown". Your "knowns" are the following: 1)You have chess pieces set at initial positions, 2)You know where you want these chess pieces to go (final positions), and 3)you can get info on the materials involved as they can act as "dampers", and dampers affect the vibrations. Your "unknown" is the forced vibration input (i.e. how fast each motor spins at a given time). For those of you with a calculus background, you can see that this is a second order linear equation with constant coefficients ( g(t)=ay''+by'+cy ). Thus you can set up matrices using Mathcad, etc. to crunch the math...solving for the motor inputs for each unit of time.