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4 questions
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Derivative with respect to vector of a function depending on vectors
I've been trying to understand this concept for hours without any success. I found similar questions on this forum (Derivative with respect to a vector is a gradient?) but I still don't understand.
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1
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3
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Why is $\nabla U(r) = \frac{dU(r)}{dr} \nabla r$?
Does anyone have a proof for the equation:
$$\nabla U(r) = \frac{dU(r)}{dr} \nabla r$$
Where $r=|{\bf r}|$ is the distance and $U(r)$ is a potential for a central force.
This is from page 13 of "...
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2
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3
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Potential energy with constraints moving body
I know that for conservative forces $\vec{F}=-\nabla{U}$. Let's consider the case of gravitational potential energy, I know that $U=mgy$. Just to check: $\vec{F}=-\nabla{U}=(0,-mg)$: perfect!
Now, let'...
3
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2
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718
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What does $\textbf{f} = -\boldsymbol{\nabla} u$ mean in practice and how is it computed?
In classical computer simulations such as molecular dynamics (MD) simulations, one integrates Newton's equations of motion to determine particle trajectories. If we think of Newton's Second Law as ...
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