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Question: Solution to system of linear equations

Question:Solution to system of linear equations

Jesse Gohl 20 Maple
linear solve linear-algebra
December 25 2007
0
The attached file is an example of a set of equations that define a gearbox composed of 4 planetary gearsets. The first 4 equations are the kinematic constraints. Where "r" indicates the size the sun or ring gear and "w" is the speed of the sun, ring, or carrier. The next 4 equations simply define new parameters (R_n) for the ratio between the size of the ring and sun gears. The last 5 equations define how these gears are connected. My question is how can I (or is it possible) to complete this worksheet in a generic way to solve for the speeds of any of the nodes in terms of some defined list of nodes and the parameterized gearbox sizes? In this example, there are 3 degrees of freedom so I might wish to solve for w[R3] (a dependent variable) in terms of w[R1], w[S2], w[S4] (independent variables), and all the parameters. The generic part comes from needing to be able to change the last 5 equations (including adding or subtracting equations) and perhaps the list of dependent and independent variables. I realize this is probably trivial with Maple so I'm sure you can guess that I'm completely new to using Maple. My experience so far has been to manually define the "solve" and "subs" commands to simplify the equations into the form that I need but of course, if the equations that define the connections change, these commands would need to be redefined. It seems that there should be a function that has as its arguments the system of equations, the list of independent variables, the list of parameters, and a list of the dependent variables that are to be solved for. Of course because of my inexperience with Maple I'm not even sure if this is a reasonable question or if this is the appropriate forum to ask it. Here's the example file: View 7210_planetary_eqs.mw on MapleNet Thanks for any help Jesse
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