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Graduate Courses Lecture

Eight Lectures on Dynamics

  • Instructor

    K. C. Park, University of Colorado Boulder, Colorado, USA

  • Class Schedule

    TBD (90 minutes/once a week) 23 March- 22 May 2026

  • Lecture Contents

    - Lect1:
    Principles in Dynamics (From Galileo to Hamilton)
    Hellenic Period: Pythagoras, Archimedes, Euclid
    Renaissance Period: da Vinci, Copernicus, Galileo, Huygens, Kepler
    Enlightenment Period: Descartes, Newton, Leibniz, Euler, D’Alembert, Lagrange
    19th Century: Hamilton, Jacobi, Poincaré
    20-21th Century: Argyris, Clough, Courant, Kalman, Kolmogorov, Lyapunov,
    Newmark, von Kármán, Zienkiewicz

    - Lect2:
    Discrete Models of Linear and Nonlinear Problems
    Euler-Lagrange Equations
    Hamilton’s Principle, Hamilton’s Action Integral
    FEM Approximations of typical dynamical systems

    - Lect3:
    Essential Linear Algebra for Dynamics

    - Lect4:
    Dynamics Response Analysis Methods
    Classical mode superposition methods
    Symplectic and variational time integrators
    Multistep time integration methods

    - Lect5:
    Reduced-Order Modeling and System Identification
    Reduced-order modeling of dynamical systems
    Markov Process on data processing
    System realization algorithms via feedback theory

    - Lect6: Multi-Physics Problems
    Fluid-structure interactions
    Thermal-structure interaction
    Control-structure interaction

    - Lect7:
    New FEM Formulations and Applications
    PartStiff method that does not require FEM assembly
    PartFlex method as the dual of PartStiff for TOP
    Large-scale solvers based on PartStiff and PartFlex methods

    - Lect8:
    Dynamic Programming and Reinforcement Learning
    Hamilton-Jacobi-Bellman(HJB) Equation
    Dynamic Programming via HJB Equation
    Reinforcement Learning algorithm(s) via Dynamic Programming