Recent content by wrobel

##\mathbb{R}^\mathbb{R}## is the space of all functions from ##\mathbb{R}## to ##\mathbb{R}##. What do you mean by writing $$\int_a^xf(t)dt$$ with ##f## non- measurable ?

I still do not understand what's wrong with the standard $$\int f(x)dx:=\{F\in C^1(a,b)\mid F'(x)=f(x),\quad x\in(a,b)\},$$ $$\quad f\in C(a,b).$$

I remembered a pretty high school problem from kinematics. But it seems it can help even undergraduates to develop their understanding of what a relative motion is. Consider a railway circle of radius ##r##. Assume that a carriage running along this circle has a speed ##v##. See the picture. A...

yes I agree. Then the only possibility I see is to write equations of equilibrium for each rod.

I have got the same and my guess is that the internal force must be Ox

A reaction in the hinge O has two components. A reaction in the hinge A has only a vertical component. We have three unknowns. Find them first by considering the equations of equilibrium for the whole construction as a rigid bod

Try to write down the equations of equilibrium for each L-like rigid body. You have three scalar static equations for a rigid body in a planar problem. There are 2 unknown components of a reaction in each hinge and 12 static equations for 4 rigid bodies. The number of equations and the number...

Céline Dion - O Holy Night

Definition of what? If you want to say that pseudovectors arise only as the cross product in 3D then that is a mistake: there is a broad theory of pseudotensors in arbitrary manifolds. Study the Hodge star operation, study what the tensor density is. In particular, there is no problem to...

OK, solve the following problem without pseudovectors and show me a gain from the bi-vector's language usage. A coin of radius ##r## rolls about a cone without slipping. At a moment ##t=t_0## the value of acceleration of the coin's lowest point ##A## is given: ##a=|\boldsymbol a_A|##. Find...

Thanks a lot. citation from this wiki article: A discontinuous linear operator in the finite dimensional space. That's nice indeed. Besides this ignorance I do not see any issues with use of pseudo tensors. The example from the article with angular momentum is irrelevant as well. Both sides...

Please bring a concrete example of a problem from classical mechanics (we are discussing classical mechanics in this thread are not we?) that provides the issues you are speaking about.

A transformation ##(p,q)\mapsto (p,2q)## preserves the Hamiltonian form of the equations but in accordance with the standard definition it is not canonical. The same story is for the Landau Lifshitz vol. 1

I must apologize, I have just looked through "Surely You're Joking, Mr. Feynman" In this text he definitely says that he learnt this technique from a textbook of analysis. It seems I was guided by this google

Feynman also said that he invented the differentiation of an improper integral to calculate it. He must have worked under the pseudonym Euler in the 18th century as well.