Inverted Pendulum on a Cart -- Nonlinear State Space equations

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SUMMARY

The discussion focuses on deriving the nonlinear state space equations for an Inverted Pendulum on a Cart system, specifically with two degrees of freedom represented by the variables x, x_dot, theta, and theta_dot. Key parameters include the mass of the pendulum (m), mass of the cart (M), length of the pendulum line (L), gravitational acceleration (g), friction (d), and the force applied to the cart (u). The user references MATLAB code that successfully implements the system but seeks clarification on the derivation of the equations. Various state space equations found in research are noted as differing, indicating a need for a standardized approach.

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  • Understanding of nonlinear dynamics
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elecboss
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Hi good day. I am trying to find the general Inverted Pendulum on a cart nonlinear state space equations with two degrees of freedom with x, x_dot, theta, theta_dot which represents displacement, velocity, pendulum angle from vertical, angular velocity. However from research, I am seeing different state space equations. In the image attached is Matlab code I found that gives the proper functionality but I am not sure how it was derived.
y-state
m-mass of the pendulum
M- mass of the cart
L- length of pendulum line
g- gravity
d- friction
u- force on cart
The other image shows the closest set of equations I found but I am unsure. Please help thank you.

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