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This Concept Map, created with IHMC CmapTools, has information related to: underactuation_course_summary, DT dynamics assumption transversality, hybrid dyamics elements guard = manifold = switching variable, Path planning via Bezier polynomial optimization with the boundary conditions for the energy efficiency (constraint optimization) Bezier calculation - derivations, output dynamics w. holonomial conditions constitute of control variable - desired variable, Lecture summary key concepts hybrid dyamics, virtual constraints = io-linearization control = output dynamics on the zero manifold apply the io-linearization: internal dynamics => what we really care. Reduced order of the system => dynamics inside the zero-manifold, CT dynamics: ODE background knowledge lagrangian ODE solver, hybrid dyamics elements CT dynamics: ODE, CT dynamics: ODE stability control equilibrium point, limit cycle & Lyapunov stability -> see if the eigen values are in OLHP, DT dynamics background knowledge conservation of moment + impact dynamics (GRF), DT dynamics assumption floating based coordinate, virtual constraints = io-linearization control = output dynamics on the zero manifold background knowledge Lie algebra, hybrid dyamics elements DT dynamics, Lecture summary key concepts Path planning via Bezier polynomial, virtual constraints = io-linearization control = output dynamics on the zero manifold apply the io-linearization: output dynamics w. holonomial conditions, Lecture summary key concepts virtual constraints = io-linearization control = output dynamics on the zero manifold, control variable - desired variable desired variable, trajectory Path planning via Bezier polynomial, DT dynamics stability control fixed point, Poincare map as for:find the stability of a fixed point by numerical analysis -> see if the eigen values are within the unit circle