StanfordASL / neural-network-lyapunov

Synthesizing neural-network Lyapunov functions (and controllers) as stability certificate.
MIT License
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Add equation of motion for the pole/end-effector system. #399

Closed hongkai-dai closed 2 years ago

hongkai-dai commented 2 years ago

This change is Reviewable

lujieyang commented 2 years ago

doc/pole_balance.tex, line 29 at r5 (raw file):

The total kinetic energy of the system is
\begin{multline}
  T = 0.5 m_e (\dot{x}_A^2 + \dot{y}_A^2 +\dot{z}_A^2) + 0.5 m_s(\dot{x}_A^2 + \dot{y}_A^2 + \dot{z}_A^2 + \dot{x}_{AB}^2 + \dot{y}_{AB}^2 + \frac{l^2(x_{AB}^2\dot{x}_{AB}^2 + y_{AB}^2\dot{y}_{AB}^2 + 2x_{AB}y_{AB}\dot{x}_{AB}\dot{y}_{AB})}{l^2-x_{AB}^2-y_{AB}^2}\\

extra l's haven't been removed here

lujieyang commented 2 years ago

doc/pole_balance.tex, line 24 at r5 (raw file):

      \dot{x}_A + \dot{x}_{AB}\\
      \dot{y}_A + \dot{y}_{AB}\\
      \dot{z}_A - \frac{lx_{AB}\dot{x}_{AB} + ly_{AB}\dot{y}_{AB}}{\sqrt{l^2-x_{AB}^2 - y_{AB}^2}}

extra l's haven't been removed here