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Short Bio:
I hold a B.A.Sc. and Ph.D. in Systems Design Engineering from the University of Waterloo, where I now serves as an adjunct professor. My research focuses on the symbolic modeling of multibody mechatronic systems. Before joining MotionPro in 2006, I worked at the Canadian Space Agency as a post-doctoral fellow, developing tools for modeling robotic manipulators. Upon joining MotionPro, I primarily worked to enhance the multibody engine of their flagship product, DynaFlexPro. Since August of 2007, when this software was aquired by MapleSoft, I've been working to help integrate this engine into MapleSoft's newest product, MapleSim. Fun stuff :-).
Research:
Multibody dynamics is the study of multi-dimensional mechanical systems comprised of rigid and/or flexible bodies interconnected by kinematic joints and/or spring-damper connections. One of the goals of multibody dynamic research is to automatically generate the governing equations of motion for a given system. To this end, numerous symbolic and numeric formulations have been developed that systematically produce equations that describe the motion of a system from a description of the system's components and the interconnections between them (topology).
The equations generated by symbolic formulations offer significant advantages during simulation. Not only can simplifications be performed on these equations, but additionally, symbolic equations only need to be formulated once for each specific system topology. Numeric formulations generate equations at each time step.
A common drawback of this approach is the complexity of the generated symbolic expressions. My research focuses on ways to intellegently formulate these equations so as to minimize both the formulation and execution time for the system. Specifically, I'm continuing to explore the use of graph-theoretic methods to generate the equations of motion for multibody systems.
One feature of this approach is that it allows for the systematic separation of terminal equations (equations describing how individual components interact) from topological equations (equations describing how components are connected). This is significant because by intelligently managing the topological equations, a multibody engine can directly control the state variables for a given system. Since the nature and number of the equations of motion are a direct result of the chosen state variables, controlling the state variables gives the multibody engine control over equation complexity during the equation formulation process.
Selected Publications:
Refereed Journal
C. Schmitke, K. Morency and J. McPhee, Using Graph Theory and Symbolic Computing to Generate Efficient Models for Multibody Vehicle Dynamics, Proc. IMechE, Part K: J. Multi-body Dynamics, 222(K4), 2008 pp. 339-352
H. S. Vogt, C. Schmitke, K. Jalali, J.McPhee, Unified Modelling and Real-time Simulation of an Electric Vehicle, International Journal of Vehicle Autonomous Systems, vol. 8, no. 3-4, 2008, pp. 288 - 307
C. Schmitke and J. McPhee, Using Linear Graph Theory and the Principle of Orthogonality to Model Multibody, Multi-domain Systems, Advanced Engineering Informatics, vol. 22, 2008, pp.147-160.
C. C. Schmitke and J. McPhee, Modelling Multibody Mechatronic Systems using Symbolic Subsystems, Multibody System Dynamics, vol. 14, no.1, 2005, pp. 81-110.
J. McPhee, C. Schmitke and S. Redmond, Dynamic Modelling of Mechatronic Multibody Systems with Symbolic Computing and Linear Graph Theory, Mathematical and Computer Modelling of Dynamical Systems, vol.10, no.1, 2004, pp.1-23.
L. Sass, J. McPhee, C. Schmitke, P. Fisette, and D. Grenier, A Comparison of Different Methods for Modelling Multibody Systems with Electrical Drives, Multibody System Dynamics, vol. 12, no.3, 2004, pp.209-250.
C. Schmitke and J. McPhee, Effective use of Subsystem Models in Multibody and Mechatronic System Dynamics, International Journal for Multiscale Computational Engineering, vol.1, no.2, 2003, pp.139-159.
Refereed Conference (Full-length Papers)
K. Morency, J. McPhee, and C. Schmitke, Symbolic Modeling of Vehicle Dynamics: A Maple Implementation, Proceedings of Maple Conference 2005, 12 pages.
W. Zhou, D. Jeffrey, G. Reid, C. Schmitke, and J. McPhee, Implicit Reduced Involutive Forms and Their Application to Engineering Multibody Systems, International Workshop on Geometric Invariance and Applications in Engineering, Xi’an, China, May 2004, 13 pages.
C. Schmitke and J. McPhee, Modelling Mechatronic Multibody Systems using Symbolic Subsystem Models, CD-ROM Proceedings of Multibody Dynamics 2003, Lisbon, Portugal, July 2003, 20 pages.
J. McPhee, S. Redmond, and C. Schmitke, Dynamic Modelling of Mechatronic Multibody Systems with Symbolic Computing and Linear Graph Theory, CD-ROM Proceedings of 4th Mathmod, Vienna, Austria, February 2003, pp.854-863.
J. McPhee, S. Redmond, and C. Schmitke, Kinematic and Dynamic Modelling of Multibody Systems, Proceedings of Maple Summer Workshop, Waterloo, Ontario, July 2002, 15 pages.