# Questions tagged [constrained-dynamics]

A constraint is a condition on the variables of a dynamical problem that the variables (or the physical solution for them) must satisfy. Normally, it amounts to restrictions of such variables to a lower-dimensional hypersurface embedded in the higher-dimensional full space of (unconstrained) variables.

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### Deriving D'Alembert's Principle

The wiki article states that D'Alembert's Principle cannot derived from Newton's Laws alone and must stated as a postulate. Can someone explain why this is? It seems to me a rather obvious principle.
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### What exactly is a virtual displacement in classical mechanics?

I'm reading Goldstein's Classical Mechanics and he says the following: A virtual (infinitesimal) displacement of a system refers to a change in the configuration of the system as the result of any ...
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### What are holonomic and non-holonomic constraints?

I was reading Herbert Goldstein's Classical Mechanics. Its first chapter explains holonomic and non-holonomic constraints, but I still donāt understand the underlying concept. Can anyone explain it to ...
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### Reduction of Nambu-Goto action to true degrees of freedom

I) First consider the point 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 $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau.$$ ...
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### Free body diagram of block on accelerating wedge

Consider the following system: I am thoroughly confused about certain aspects of the situation described in this diagram in which a block is placed on a wedge inclined at an angle Īø. (Assume no ...
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### Holonomic constraints and degrees of freedom

Wikipedia and other sources define holonomic constraints as a function $$f(\vec{r}_1, \ldots, \vec{r}_N, t) \equiv 0,$$ and says the number of degrees of freedom in a system is reduced by the ...
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### Confusion with Virtual Displacement

I have just been introduced to the notion of virtual displacement and I am quite confused. My professor simply defined a virtual displacement as an infinitesimal displacement that occurs ...
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### Non-relativistic QFT Lagrangian for fermions

Take the ordinary Hamiltonian from non-relativistic quantum mechanics expressed in terms of the fermi fields $\psi(\mathbf{x})$ and $\psi^\dagger(\mathbf{x})$ (as derived, for example, by A. L. Fetter ...
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### Why are Hamiltonian Mechanics well-defined?

I have encountered a problem while re-reading the formalism of Hamiltonian mechanics, and it lies in a very simple remark. Indeed, if I am not mistaken, when we want to do mechanics using the ...
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### Derivation of Lagrange Equations from Newton's Second Law for a Non-holonomic System of Particles

I am interested to write down a derivation of Lagrange equations from Newton's second law for a non-holonomic system of particles. Here, I mention my derivation where I am stuck right at the last step....
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### How to find Hamiltonian from this simple Lagrangian? (tricky)

$$L~=~ \frac{1}{2} \dot{q} \sin^2{q}$$ Is it zero or not defined?
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### Missing terms in Hamiltonian after Legendre transformation of Lagrangian

Short question Given any Lagrangian density of fields one could possibly conceive, is it the case that after one has performed a Legendre transformation, if the Hamiltonian is then expressed in terms ...
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