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Symbolic Mechanics: Designing a Better Trebuchet and Illustrating Chaos

Phil Todd

Wolfram Technology Conference 2013
Conference location

Champaign, Illinois, USA

Mechanical Expressions is new symbolic mechanics software which allows the user to draw a mechanical system and which outputs symbolic expressions for static, kinematic and dynamic quantities. These mathematical expressions may be exported to Mathematica for further analysis. Entire Mechanical Expressions models may also be exported as Mathematica Dynamic Modules. We illustrate both types of interaction in the context of some simple mechanical models.

As an example of a simple chaotic machine, a mass m acts as a pendulum, and is attached with a spring to a mass M which is allowed to slide along a horizontal rod. A simple model of the machine has variables for geometric parameters and also for the physical quantities: mass, spring rate and natural length. Equations for the acceleration of the model geometric parameters are generated automatically by Mechanical Expressions and may be cut and pasted into Mathematica. The full range of Mathematica's differential equation solving and visualization capabilities may then be applied. For example, applying ParametricNDSolveValue[] and Manipulate[] gives a compelling demonstration of the onset of chaos in this simple device. The chaotic motion itself may be visualized in a Dynamic Module in Mathematica, or exported as a JavaScript app directly from Mechanical Expressions.

*Wolfram Technology

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