# Search results

1. ### I Basic question about variational calculus

yes, and that is exactly the case under consideration.
2. ### Tensor Differentiation

Just some remarks. 1) ##b_{ij}x_j## is not a tensor at least this expression does not keep its shape under changes of variables 2) the operation ##\partial/\partial x_i## takes tensors to not-tensors 3) if only linear changes are considered ##x_i=c_{ij}x'_j## then everything is ok
3. ### I D'Alembert's principle vs Hamilton's principle

yes, that is the point that's a key mistake. They are not equivalent. In the case of nonholonomic constraints the Hamilton principle implies vaconomic equations. I can only again refer you to the books cited above.
4. ### I D'Alembert's principle vs Hamilton's principle

There is a funny story as well. I think only Russians know it. Very long ago before the famous many valued Landau and Lifshitz textbook appeared, Landau and Pitaevsky wrote a textbook on classical mechanics. This book contained many errors and it was completely smashed by Fok in his article...
5. ### I D'Alembert's principle vs Hamilton's principle

the solution ##x_*(t)## to the variational problem described in #11 satisfies the equation $$\frac{d}{dt}\frac{\partial \mathcal L}{\partial \dot x^k}-\frac{\partial \mathcal L}{\partial x^k}=0,\quad \mathcal L=L+\lambda_k(t)a^k_s\dot x^s$$ this equation contains ##\dot\lambda## and it is not...
6. ### I Basic question about variational calculus

for a function of a single variable that is the same
7. ### A Something on Baire categories

There is an assertion that follows from very general theorem directly and I do not understand if this assertion trivial or it may be of some interest. The assertion is enclosed below please comment

24. ### A The equations of variable mass systems

now we can turn back to https://www.physicsforums.com/threads/what-is-the-tension-of-the-rope.1004390/#post-6506923 :)
25. ### A The equations of variable mass systems

I think you just missed ##\rho## and the formulas must be as follows
26. ### A The equations of variable mass systems

The equations of variable mass systems are usually deduced from some very informal argument. It is so at least for the books I know. So I tried to construct a formal proof based on the continuous media equations. Criticism, remarks etc are welcomed. Let ##D\subset \mathbb{R}^q## be an open...
27. ### What is the tension of the rope?

for the velocity the variable mass equation gives the same , I did not check for the force
28. ### What is the tension of the rope?

sure it is just incorrect to apply the standard Newton law to a variable mass system it is the acceleration of the center of mass who can not exceed g
29. ### What is the tension of the rope?

The one-dimensional fall of a folded chain with one end suspended from a rigid support and achain falling from a resting heap on a table is studied. Because their Lagrangians contain no explicittime dependence, the falling chains are conservative systems. Funny argument little bit. Why do that...
30. ### What is the tension of the rope?

Something like that I guess