# cart

dynamic equations for cart benchmark model

## Contents

- Syntax
- Description
- Input Arguments
- Output Arguments
- See Also

## Syntax

f = cart(x, u, w)

## Description

Dynamic equation for the cart benchmark model. The benchmark represents a cart that is coupled to the environment by a spring and a damper, where both the stiffness of the spring and the damping of the damper are nonlinear functions of the cart position. The system states are the position and the velocity of the cart. The input to the system is an external force acting on the cart.

## Input Arguments

x | system states x (dimension: [nx,1])
u | control inputs u (dimension: [nu,1])
w | disturbances w (dimension: [nw,1])

## Output Arguments

f | value of the dynamic function = time derivative of x

## See Also

`car`, `doubleIntegrator`, `robotArm`

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