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added some $'s
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Gjergji Zaimi
Gjergji Zaimi
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As you may know, if a system can be written in the form:

\dot{\mathbf{x}}= -\bigtriangledown V$$\dot{\mathbf{x}}= -\bigtriangledown V$$

for some continuously differentiable, single-valued scalar function V(x)$V(x)$. such a system is called gradient system with potential function V$V$.

The question is that having the gradient system, how can one find its potential function?

As you may know, if a system can be written in the form:

\dot{\mathbf{x}}= -\bigtriangledown V

for some continuously differentiable, single-valued scalar function V(x). such a system is called gradient system with potential function V.

The question is that having the gradient system, how can one find its potential function?

As you may know, if a system can be written in the form:

$$\dot{\mathbf{x}}= -\bigtriangledown V$$

for some continuously differentiable, single-valued scalar function $V(x)$. such a system is called gradient system with potential function $V$.

The question is that having the gradient system, how can one find its potential function?

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Kamran Bigdely
Kamran Bigdely
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How do you find the potential function V of the gradient system?

As you may know, if a system can be written in the form:

\dot{\mathbf{x}}= -\bigtriangledown V

for some continuously differentiable, single-valued scalar function V(x). such a system is called gradient system with potential function V.

The question is that having the gradient system, how can one find its potential function?