[Introduction | Background | Results | Conclusions]


The model is of the shock absorbers of a car. x represents the position and y the velocity of the shock absorbers. z and w represent forcing terms. z and w can be uncoupled from the other two to show that they are sinusoidal if: lambda > 0 and zero otherwise.

There is only one point where it is possible that x,y,z,w can all be constant and that is at the origin of our four dimensional system. We determined that the origin can be either a sink, source, or saddle. The physical interpretations of this information is important because the model should have interpretations that lead to physical understanding.

Our exploration of this model is very limited because we only varied two of the constants. An attempt to fully analyze the system would require quite an effort but it would be necessary to go the full length if all possible behavior of the system is to be uncovered. Otherwise only a partial picture can be gleaned.

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Michelle Vadeboncoeur <mrvahs@wpi.edu>
Forest Lee-Elkin <yusuf@wpi.edu>