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### How do non-conservative forces affect Lagrange equations?

If we have a system and we know all the degrees of freedom, we can find the Lagrangian of the dynamical system. What happens if we apply some non-conservative forces in the system? I mean how to deal ...
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### Hamilton's principle and virtual work by constraint forces

I have a question about the following pages(pg 47 and 48) from Goldstein's "Classical Mechanics" I do not understand how (2.34) shows that the virtual work done by forces of constraint is zero. How ...
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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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### Can the Lagrange multiplier method be used with non-holonomic constraints?

The confusion for me comes from page 46 of Goldstein, where he says "However, it has been proven that no such varied path can be constructed unless [the differential equations of constraint] are ...
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### Conversion of non-holonomic constraints to holonomic

In the case of a disc rolling without slipping, we have a constraint $\dot{x}=a\dot{\theta}$ where $a$ is the radius of the disc. Note that I have considered $x$ and $\theta$ as the generalized ...
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### When the constraints are not holonomic, why is it not possible to find such $q_i$s that $\delta q_i$s are independent of each other?

In the book of Classical Mechanics by Goldstein, at page 20, it is given that However, I cannoot understand from what has been presented so far that when the constraints are not holonomics, why is it ...
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### Non-holonomic constraints, degree of freedom and generalized coordinates

If a system has $N$ coordinates and $M$ number of holonomic constraints then number of degree of freedom $=N-M$ and generalized coordinates $=N-M$ too. But if there are $k$ non-holonomic constraints ...