## Physical Modeling - Killer Application No. 2 for Symbolics

For almost 20 years, Math education has been recognized as the first killer application for symbolic computing. By taking out the grunt work of manipulating equations, calculating integrals and performing matrix computations with symbolic entries, systems such as Maple have transformed the math classroom.

Now, finally, a second killer application for symbolic computing is emerging. Physical Modeling is about building system-level simulation models to verify a design before producing hardware, thus saving cost and speeding up development cycles. Physical Modeling tools like MapleSim allow you to build virtual prototypes by connecting components from a large pre-built library from multiple domains: Electrical, Mechanical, Thermal, etc. The simulation-models are “system-level”, which means that we are interested in the overall system behaviour as opposed to doing a detailed analysis of a particular nature (the realm of CFD and FEA systems).

The physical components in the MapleSim library represent actual parts - an electrical resistor, a pump, a rotational joint, a clutch, etc. Under the hood, each of these components carries the mathematical equations that describe its dynamic behaviour. Drawing a connection between two or more components represents a physical connection and thus carries physical quantities: electrical charge, torque, acceleration, etc. Each such connection implies an additional set of equations, describing how the components interact.

As you can imagine, if you build an even moderately complex model, the total size of the mathematical equations that you will need for simulation grows very rapidly. Using symbolic techniques to simplify the equations before they are solved numerically becomes the crucial ingredient. It is this pre-processing at the equation-level which is responsible for huge speed-ups when compared to traditional, mainstream tools that rely solely on numeric solving. For example, it is not uncommon for code generated from a MapleSim model to run fifty times faster than was possible before and thus enable a new level of faithfulness for hardware-in-the-loop applications.

Symbolic computing has long been perceived to be too slow for real-world engineering applications. Now we know that a state-of-the-art symbolic engine is able to dramatically increase the speed of a numeric simulation, drive productivity and challenge the established engineering tool chain. A true killer application.

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