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  1. wrobel

    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
  2. wrobel

    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...
  3. wrobel

    A The stress tensor

    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.
  4. wrobel

    I Rigid body with fixed point

    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...
  5. wrobel

    I Request for a reference

    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...
  6. wrobel

    A Something about configuration manifolds in classical mechanics

    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...
  7. wrobel

    Untranslatable words

    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...
  8. wrobel

    A The Method of Characteristics

    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 :)
  9. wrobel

    A Two disks -- An educational problem

    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...
  10. wrobel

    A About the Noether theorem

    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...
  11. wrobel

    Writing a paper

    Stupid question. Is that possible form the style and language viewpoint to write such things in the article: is the environment "Fact" ok?
  12. wrobel

    Non interesting story 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...
  13. wrobel

    A On a formal viewpoint on the D’Alembert–Lagrange Principle

    I would like to discuss the following article: 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...
  14. wrobel

    A The Lagrange–d'Alembert principle for rigid bodies

    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...
  15. wrobel

    A The unwinding coil (teaching experience sharing)

    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...
  16. wrobel

    Two cylinders rotating with contact at an angle (reformulation of the problem)

    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...
  17. wrobel

    A Where to publish a paper

    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
  18. wrobel

    Jumping tractor

    Just an effect interesting to think about:
  19. wrobel

    Phys Challenge

    What about Physics Challenges similar to Math Ones? Sorry if it is inappropriate place for this topic
  20. wrobel

    A Connections and distributions

    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?
  21. wrobel

    Problems with English

    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...
  22. wrobel

    Classical Monographs

    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...
  23. wrobel

    Insights A Pure Hamiltonian Proof of the Maupertuis Principle - Comments

    Greg Bernhardt submitted a new blog post A Pure Hamiltonian Proof of the Maupertuis Principle Continue reading the Original Blog Post.
  24. wrobel

    A grasshopper on a straw

    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...
  25. wrobel

    What did Einstein mean (discussing success): "and z is keeping your mouth shut"

    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"
  26. wrobel

    Inverse square potential

    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 ?
  27. wrobel

    A Ergodic theorems

    Is that possible to derive the Birkhoff Ergodic Theorem from or with the help of the Von Neumann ergodic theorem?
  28. wrobel

    Servo-Constraints in Mechanics - Comments

    Greg Bernhardt submitted a new blog post Servo-Constraints in Mechanics Continue reading the Original Blog Post.
  29. wrobel

    I Bounded Curves

    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...
  30. wrobel

    A Periodic solutions in a mechanical system

    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...