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2

Let me call radial stability the stability of $r$ around $r_0$, where $r_0$ is the radius of the circular orbit. The difference between this one and the Lyapunov stability is that the latter looks not only to $r$ but also to the polar angle $\theta$ (for a central force) and their conjugated momenta. So in this sense I would say Lyapunov is stronger. ...


10

A long rod, especially with additional masses at the ends, has a large moment of inertia and therefore can change its angular velocity only slowly. This means that if the walker gets off-balance, there is more time available to correct before he falls.


-1

Both are unstable (ring and sphere) for the same reason: the potential everywhere inside either one is zero. This is true for gravitational as well as electrical and magnetic forces, which are all inverse square law / central force situations, and it is that pattern which causes the result. The proof requires calculus, but is considered an elementary ...


2

Flexibility plays no role, because the rod can be naturally bent. If the walker has no rod and his CoM is not aligned to the rope he hasn't a big chance of adjusting it. A rod contributes to the mass of the system (and the position of CoM) and distribute mass on a greater extension, and the man can shift it sideways or rotate it. Angular momentum mvr = L ...


0

Sorry but I think this question is "off topic" : it is about civil engineering, and asks how to calculate something; it does not ask for an explanation of a specific physics concept. See the site policy at http://physics.stackexchange.com/help/on-topic. It is quite difficult to predict the effect of the wind on such a diverse structure - you need to ...



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