# Tagged Questions

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### Teenager solves Newton dynamics problem - where is the paper?

From Ottawa Citizen (and all over, really): An Indian-born teenager has won a research award for solving a mathematical problem first posed by Sir Isaac Newton more than 300 years ago that has ...
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### Why isn't the 3 body problem solvable?

I'm new to this "integrable system" stuff, but from what I've read, if there are as many linearly independent constants of motion that are compatible with respect to the poisson brackets as degrees of ...
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### Show velocity of a particle during its flight at time $t$

I'm completely stuck, I think I have to use Newton's second law but I have no idea where to start, any help would be appreciated! At time $t=0$ a particle of unit mass is projected vertically upward ...
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### What exactly is meant by 'Integrate the Equation of Motion'?

Short Question: if a question says to 'integrate the equation of motion', what does it mean? Long Question: Question: Take a planet of mass $M$ and place a satellite at rest at a distance $R$ ...
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### How can I put the “3 body problem” mathematically?

I'm trying to put the 3 body problem mathematically. But I don't know how. I always get something reasonable, but I get something that is wrong.
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### Restricted Three-Body Problem

The movement of a spacecraft between Earth and the Moon is an example of the infamous Three Body Problem. It is said that a general analytical solution for TBP is not known because of the complexity ...
Suppose we have a mechanical system with 1 degree of freedom, i.e. an ODE $$(1)\quad \ddot{q}+V^\prime(q)=0,$$ where $V \colon \mathbb{R} \to \mathbb{R}$ is some smooth function (potential ...
### Why does acceleration = $v\frac{dv}{dx}$
If we define $x$ = displacement, $v$ = velocity and $a$ = acceleration then I am used to the ideas that $a= \frac{dv}{dt} = \frac{d^2x}{dt^2}$ However I also understand $a=v \frac{dv}{dx}$. Can ...