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Work through conservative-force and single-particle dynamics examples in one, two, and three dimensions, including gravity, springs, projectiles, and pendulums.
Work through the transport theorem for vector derivatives in rotating and translating reference frames using cannon, turntable, Earth, and oscillatory-motion examples.
Introduces spacecraft reference frames and satellite viewing geometry, including access areas, swath width, and ground tracks.
An introduction to Hamiltonian mechanics explains its advantages over the Lagrangian formalism and derives Hamilton’s canonical equations from Lagrange’s equations.
Explore how saddle-node, SNIPER, and homoclinic bifurcations create or destroy limit cycles, including scaling laws for their amplitude and period.
Extends one-dimensional bifurcation ideas to two-dimensional systems, using nullcline geometry and center manifolds to analyze saddle-node, pitchfork, and transcritical changes.
Use the Poincaré-Bendixson theorem to construct trapping regions and prove stable limit cycles in planar systems, including a glycolysis oscillator.
Analyze a spruce budworm population model to see how one-dimensional dynamics produce bistability, saddle-node bifurcations, and a cusp catastrophe.
Explore coupled rigid bodies, angular momentum, impulsive dynamics, and changing geometry through examples from cats, lizards, spacecraft, ships, and ants.
Learn how quasivelocities and Kane’s method eliminate Lagrange multipliers when deriving constrained mechanical systems’ equations of motion.
Analyze how normal modes reveal natural frequencies and mode shapes, and how resonance can amplify forced vibrations to failure.
Explores nonholonomic motion through rolling coins, bicycles, fish, and rattlebacks, then derives normal modes and natural frequencies for small oscillations.
Explore Coulomb friction through live coefficient measurements, phase portraits, nonsmooth mechanics, and reduced-order analysis of a spinning symmetrical top.
Learn how Routhian reduction uses cyclic coordinates, conserved generalized momenta, and physical symmetries to simplify mechanical systems.
Derive constraint forces with Lagrange multipliers, then apply nonholonomic dynamics to wheeled systems and rolling bodies in a downhill race.
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