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To get a sense of how symbolic computing can be applied to problems in multibody dynamics and control system design, download some the following tutorial notebooks. If you are not yet a Mathematica user you can read and print the notebooks with MathReader.

• Dynamics: An overview of the model building process with examples. Includes multibody systems with flexible bodies and nonholonomic constraints.

• Controls: A summary of linear and nonlinear control design tools. Includes adaptive control systems.

• Manifolds: Illustrates functions for constructing local parametric representations for implicitly defined manifolds. Illustrates computation of equilibrium surface of aircraft near stall points.

• Variable Structure Control: Tools for the design of Variable Structure Controllers are described. Includes the use of smoothing and moderating functions.

• Backlash: Illustrates the inclusion of nondifferentiable elements in mechanical models, e.g. impact and backlash, discontinuous friction.

• Friction Example: This notebook documents the computations for the example in the paper "Variable Structure Control of Systems with Uncertain Nonlinear Friction," by Kwatny, Teolis and Mattice, Automatica, Vol. 38, July 2002, pp.1251-1256.

• Observable and Observer Form Examples: This notebook illustrates the construction of observable and observer forms for several locally observable affine systems. Some of these are examples in the paper H. G. Kwatny and B. C. Chang, “Symbolic Computing of Nonlinear Observable and Observer Forms,” Applied mathematics and Computation, Vol 171, December 2005, pp. 1058-1050.

Hybrid Systems

• IP Tutorial: Provides an overview of the procedures to reduce a logical statement to a set of mathematical programming formulas.

• Dynamic Programming: Provides an overvue of functions used for dynamic programming problems. An example of an optimal load shedding strategy for a power system with induction motor loads and vital loads with UPS.

Power Systems

• Phase Portraits: Phase portraits of 2D examples.
• Power System Torus Example: Illustrates the stability of a conservative power system via energy methods under parameter variation
• Static Bifurcation: Illustrates use of NRS method for generating equilibrium curves and voltage stability limits.
• Generator MEX Functions: Illustrates MEX function assembly for synchronous machines.
• System Simulation: Illustrates network MEX function assembly and simulation for a 5 bus and a 12 bus network.