General methodology
- 1. Description of the system
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- Describe system by some parameters (positions, speed, orientation, etc).
- - State of the system is known at time \(t=0\) - Initial value problem in time
- - State of the system may be constrained in space - Boundary value problem in space
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- Link the evolution of the system to forces or constraints using dynamic principles and conservation laws
- \(\Rightarrow\) Differential equation
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- Solve the differential equation using numerical iterative approaches.
- Note: Fundamentally different that direct approach controling the trajectories at key-frames
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- - The system is set at an initial step
- - We let the numerical solution build the space-time trajectory for us
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- (+) Allows to model complex behavior
- (-) Lack of control on the result