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
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...
Inspired by the closed thread about pressure:) Here is some of my fantasies about a definition of the stress tensor. Nothing here claims to be a correct theory but just as a matter for discussion.
Today I read a book in mechanics and encountered a funny proposition about rigid body with fixed point. Perhaps somebody will be interested to propose it to students as a task. This proposition is almost correct:)
Consider a rigid body with a fixed point ##O##. Let ##Oxyz## be a coordinate...
There is a nice fact. It approximately sounds like that: Let ##H=H(p,q)## be a Hamiltonian system with ##n## degrees of freedom such that all its orbits are closed. Then the periods of all the orbits belonging to the same energy level are the same.
Please which textbook does contain this? I...
I think it could be interesting.
Consider a mechanical system
A circle of mass M can rotate about the vertical axis. The angle of rotation is coordinated by the angle ##\psi##. A bead of mass m>0 can slide along this circle. The position of the bead relative the circle is given by the angle...
In Russian there is a word that is very hard to translate in English. Vladimir Nabokov believed that there is no English equivalent. This word is пошлость (pronounces poshlost). Very approximately speaking, this word expresses a negative esthetic estimate of something which claims to be...
This just to share a teaching experience.
Questions about the method of characteristics are raised from time to time in this forum.
Hope the following text will be of some use. This is what we tell to students in courses of
analytical mechanics :)
Let me share an educational problem which I learned from my friend Prof. M. Kirsanov. Perhaps somebody finds it interesting to discuss it with students. I do.
The problem is pure kinematic.
Assume we have two disks which can rotate about their fixed centers ##A,C,\quad |AC|=b##. The radii of...
In Hamiltonian statement the Noether theorem is read as follows. Consider a system with the Hamiltonian function $$H=H(z),\quad z=(p,x),\quad p=(p_1,\ldots,p_m),\quad x=(x^1,\ldots,x^m)$$ and the phase space ##M,\quad z\in M.## Assume that this system has a one parametric group of symmetry...
https://au.news.yahoo.com/disturbing-photo-heroic-boy-saved-sister-dog-attack-051333690.html
When a six-year-old boy saw his little sister being attacked by a dog he didn’t hesitate to jump in and protect her.
Bridger from from Cheyenne, Wyoming in the US has been dubbed a hero after he...
I would like to discuss the following article: https://web.ma.utexas.edu/mp_arc/c/20/20-87.pdf
This article is pure educational and it does not contain any research level results. My aim was to build the theory of the D’Alembert–Lagrange Principle in mathematically closed and modern form...
This post is also an invitation to compose problems of the presented below type.
The Lagrange–d'Alembert principle by itself is used very seldom. It is usually used to derive the Lagrange equations and that is all. But actually it is a powerful tool in nonholonomic mechanics.
As an example...
It is just for teaching experience sharing. Consider a uniform disk. A stretchless and massless wire has been wound on the disk. The end of the wire is attached to the ceiling. Initially the system is at rest as it is shown at the picture. Then the disk is released. It falls down and rotates and...
Some time ago there was a problem with the following picture somewhere out here. I think this problem was underestimated a little bit.
Let us reformulate the problem. Assume that each cylinder, if it was not influenced by the other one, could rotate freely about its fixed axis. But the...
In what journal can I submit an educational type article with some not completely standard approach to Largangian mechanics about 15 pages long?
Sorry if this place is wrong for this thread
Hi Colleagues!
please look through the enclosed file and I have two questions about theorems 1,2
1) Are there any references? I would prefer to cite these theorems and do not bring proof
2) Do the converse theorems hold?
I live in Russia and to keep my English fit I usually download movies from torrents and watch them. I also read books. And yesterday I tried to watch movie called "Do not knock twice" (quite silly teenagers horror) just for English.
I was shocked! I understood completely nothing! When I found...
Epoch of thick textbooks in classical mechanics was ended at the edge of 19-20 century. There appear a lot of new branches of physics and classical mech. is no longer considered by physicists as a cutting-edge branch but only as an educational subject. Nevertheless, I believe that we should not...
Recently I encountered a funny thing. Consider the following problem from high school course.
A small grasshopper of mass ##m## sits on a tip of a straw. The straw is a thin homogeneous rod of mass ##M## and of length ##2l##. The straw lies on a smooth horizontal floor.
What smallest initial...
by this quote "If A is a success in life, then A equals x plus y plus z. Work is x; y is play; and z is keeping your mouth shut."
i wonder if "z" means "say nobody about your results until they are published" or "work and do not gab on empty"
Do exist examples of attraction forces with such a type potential
##V(\boldsymbol r)\sim-\frac{1}{|\boldsymbol r|^2}, \quad |\boldsymbol r|\to 0##
in physics ?
It is well known that a curve in ##\mathbb{R}^3## is uniquely (up to a position in the space) defined by its curvature ##\kappa(s)## and torsion ##\tau(s)##, here ##s## is the arc-length parameter. We will consider ##\kappa(s),\tau(s)\in C[0,\infty)##
Thus a natural problem arises: to restore...
Consider the following mechanical system
A thin tube can rotate freely in the vertical plane about a fixed horizontal axis passing through its centre ##O##. A moment of inertia of the tube about this axis is equal to ##J##. The mass of the tube is distributed symmetrically such that tube's...