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Problem in constraint equations

In this, if I want the acceleration constraint between $M$ and $2M$, I write $AM+2AB$=LENGTH OF STRING, which on differentiating twice gives $a_{m}=2a_{2m}$(which turns out to be correct). However, if ...
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Work done by internal forces of a rigid body

I am reading Goldstein's Classical Mechanics book, and I came across that: In a rigid body the internal forces do no work Is this statement based on the assumption that the internal forces are ...
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Degrees of freedom in double Atwood machine?

Why the degree of freedom in double Atwood machine (one block on one side and a pulley with one block in its each side on other side) is 2 and not 1? According to the formula $s=3*n-m$; where $n=$...
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In d'Alembert's principle, how that the Reverse effective force and Force of constraints are different?

In d'Alembert's principle, how that the Reverse effective force and Force of constraints are different? Both are opposition or restriction on the body but how both be different in real?
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What makes an equation an 'equation of motion'?

Every now and then, I find myself reading papers/text talking about how this equation is a constraint but that equation is an equation of motion which satisfies this constraint. For example, in the ...
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The consistency conditions of constrained Hamiltonian systems

I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
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Reduction of Nambu Goto action to true degrees of freedom

First consider the particle $$S=m\int\sqrt{-\dot{X}^2}d\tau$$ if you choose the static gauge $\tau=X^0$ and replace it in the action you get $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
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Position based dynamics constraint scaling factor

Reading through MÃ¼ller et al., Position Based Dynamics, 2007 I got lost when passing from equation (5) $$\Delta p = \frac{C(p)}{|\nabla_pC(p)|^2}\nabla_pC(p)$$ to equation (6) (and applying the ...
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Question on the constraint force of a string

I would like to know if the following statement is true or false even if I expect that it is true. Notation: I will consider a string that has no mass and that can not be extended. Saying that a ...
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Virtual Work- Is the presentation in Cornelius Lanczos wrong?

Book: The Variational Principles of Mechanics by Cornelius Lanczos Edition: 4th Chapter: 3, The Principle of Virtual Work I am on the second page of the 3rd chapter (pg 75; it has the Eqn. 31.1). ...
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Euler-Lagrange for constrained system

Suppose we have Euler-Lagrange system with generalized coordinate $r_1$ and $r_2$, and input $u_1$ and $u_2$. I know how to prove this system is indeed Euler-Lagrange system. Suppose now if we have a ...