# How do I represent the followin LTI equation in Laplace Representation on matlab? By hand it's done but i can't seem to make it work on matlab

The car dynamics associated with the vehicle’s speed can be expressed by the following LTI equation:

$$mdy/dt(t)=u(t)-45by(t)-45bw(t)-mg\theta(t)$$

How do I write that on MATLAB in a Laplace representation?

$$y(t)$$ is the car’s speed in m/s,

$$u(t)$$ is the engine’s propelling force,

$$w(t)$$ represents the wind speed along the car’s travelling trajectory (if $$ws(t) > 0$$ then the wind direction is opposing the car’s travelling trajectory and vice versa),

$$m = 1000 kg$$ is the car’s nominal mass,

$$g = 9.81m/s^2$$ is the gravitational acceleration constant,

$$b = 0.377$$ is the aerodynamic coefﬁcient associated with drag,

$$\theta(t)$$ is the road’s inclination angle in rad

• How to write the equation in Matlab is going to depend somewhat on what you want to do with it afterwards...also, are $w$ and $\theta$ given or do you want to get the solution in terms of them? – Ian Dec 2 at 22:02
• They’re not given, I have to get the solution in terms of them. – user731133 Dec 2 at 22:19

## 1 Answer

You cannot physically transform this LTI into a Laplace transform on Matlab. It’ll have to be done by mathematically.

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