Classical mechanics Definition and 1000 Threads

  1. deuteron

    I Constraint Forces and Lagrange Multipliers

    My question is about the general relationship between the constraint functions and the constraint forces, but I found it easier to explain my problem over the example of a double pendulum: Consider a double pendulum with the generalized coordinates ##q=\{l_1,\theta_1,l_2,\theta_2\}##,: The...
  2. deuteron

    I Intuition Behind Intermediate Axis Theorem in an Ideal Setting

    For a rigid body with three principal axis with distinct moments of inertia, would the principal axis with the intermediate moment of inertia still be unstable in ideal conditions, e.g. no gravity, no friction etc.? From the mathematical derivation I deduce that it should be unstable, since we...
  3. C

    Classical How is the book "Structure and Interpretation of Classical Mechanics"?

    I learned some computer science basics from the book SICP ( Structure and Interpretation of Computer Programs, Authors: Gerald Jay Sussman, Hal Abelson, Julie Sussman ) and I've witnessed a book about mechanics from the same author called Structure and Interpretation of Classical Mechanics...
  4. giodude

    I Using Linear Algebra to discover unknown Forces

    In classical mechanics, it seems like solving force equations are a question of finding a solvable system of equations that accounts for all existing forces and masses in question. Therefore, I'm curious if this can be mixed with reinforcement learning to create a game and reward function...
  5. Maumas

    Invariance of a volume element in phase space, What does it mean?

    The invariance of this volume element is shown by writing the infinitesimal volume elements $$d\eta$$ and $$d\rho$$ $$d\eta=dq_1.....dq_ndp_1......dp_n$$ $$d\rho=dQ_1.......dQ_ndP_1....dP_n$$ and we know that both of them are related to each other by the absolute value of the determinant of...
  6. F

    Why is the thrust equation same under gravitational force?

    The homework statement isn't exactly as is mentioned above. The actual problem statement is as follows: This is problem 3.8 from John R. Taylor's Classical Mechanics; however, my question is not related to the main problem itself but one particular aspect of it. Now, in the same textbook (John...
  7. Lagrange fanboy

    I Proof that canonical transformation implies symplectic condition

    Goldstein's Classical Mechanics makes the claim (pages 382 to 383) that given coordinates ##q,p##, Hamiltonian ##H##, and new coordinates ##Q(q,p),P(q,p)##, there exists a transformed Hamiltonian ##K## such that ##\dot Q_i = \frac{\partial K}{ \partial P_i}## and ##\dot P_i = -\frac{\partial...
  8. Anubhav singh

    Question about the Product of Inertia for a Rolling Disk

    I think product of inertia always zero because rolling motion of disk is fully balanced
  9. F

    Vertical projectile motion with quadratic drag (sign convention)

    I am attempting problem number 2.38 from John R. Taylor's Classical Mechanics and I am not getting the correct answer. My procedure is as follows: Equation of motion (taking up as the positive direction): $$m\dot{v}=-mg-cv^2$$ Now to find ##v_\mathrm{ter}##, the terminal velocity, we consider...
  10. rajsekharnath

    What are your thoughts on self-studying Goldstein?

    I am self studying Goldstein first chapter "A survey on the elementary principles", so far I have been enjoying it, sometimes he skips some lines while deriving a principle or so, therefore sometimes I get to PSE or Physics Forums to know the things I lack understanding in. What are your...
  11. rajsekharnath

    Classical Source recommendation on Differential Geometry

    I am intending to join an undergrad course in physics(actually it is an integrated masters course equivalent to bs+ms) in 1-1.5 months. The thing is, in order to take a dive into more advanced stuff during my course, I am currently studying some of the stuff that will be taught in the first...
  12. M

    How Can Rectangular Prisms Transform Billiards?

    I plan to add on to this as I have time and ability. Apologies for the weird formatting.
  13. al4n

    B Need help understanding some concepts about friction

    We have 2 objects, m1 and m[SUPlB]2[/SUB] Friction is present between the two objects but not between m1 and the floor. A force is exerted on the bottom object which causes it to accelerate parallel to the floor. The thing I'm wondering for while now is, how do I prove that the acceleration of...
  14. B

    What is the source of the Kelvin Water Dropper effect?

    From a classical mechanics perspective I understand the force interactions leading to the phenomenon, but from a matter perspective, what is a "positive" or "negative ly" charged water stream? Is this referring to the spontaneousH(+) + OH(- )formations?
  15. P

    I Why isn't the Lagrangian invariant under ##\theta## rotations?

    I just calculated the Lagrangian of a particle of mass ##m## in a radially symmetric potential ##V(r)##. I thought it would be a good idea to switch to spherical coordinates for that matter. What I get is $$ L = \frac{1}{2} m \left( \dot{r}^2 + r^2 \dot{\theta}^2 + r^2 \dot{\varphi}^2...
  16. Shreya

    The Definition of Torque - a proof

    I have been trying to understand this proof from the book 'Introduction to classical mechanics' by David Morin. This proof comes up in the first chapter of statics and is a proof for the definition of torque. I don't understand why the assumption taken in the beginning of the proof is...
  17. StenEdeback

    What is the volume of the system when inserting the 4-velocity of the observer?

    I have attempted but with no result.
  18. Reuben_Leib

    I Help with Euler Lagrange equations: neighboring curves of the extremum

    I tried writing this out but I think there is a bug or something as its not always displaying the latex, so sorry for the image. I have gone through various sources and it seems that the reason for u being small varies. Sometimes it is needed because of the taylor expansion, this time (below) is...
  19. Reuben_Leib

    I Why does ##u## need to be small to represent the Taylor expansion

    Necessary condition for a curve to provide a weak extremum. Let ##x(t)## be the extremum curve. Let ##x=x(t,u) = x(t) + u\eta(t)## be the curve with variation in the neighbourhood of ##(\varepsilon,\varepsilon')##. Let $$I(u) = \int^b_aL(t,x(t,u),\dot{x}(t,u))dt = \int^b_aL(t,x(t) +...
  20. R

    Coordinates of a point on a rotating wheel

    My issue is in deriving the coordinates of a point on a wheel that rotates without slipping. In Morin's solution he says that: My attempt at rederiving his equation: I do not understand how the triangle on the bottom with sides indicated in green is the same as the triangle on top that is...
  21. Slimy0233

    I Heating a tungsten filament to find out the maximum brightness emitted

    I was taking notes from a lecture on Quantum Physics and during the introduction, they gave an example of what led to the discovery of Quantum Physics: The electric bulb example where the brightness and colour of light depended on the temperature of the filament(see...
  22. Peter Morgan

    I The collapse of a quantum state as a joint probability construction

    The titular paper can be found here, https://doi.org/10.1088/1751-8121/ac6f2f, and on arXiv as https://arxiv.org/abs/2101.10931 (which is paginated differently, but the text and equation and section numbers are the same). Please see the abstract, but in part this 24 page paper argues that we...
  23. M

    Morin classical mechanics differential equation problem

    I was reading the oscillations chapter which was talking about how to solve linear differential equations. He was talking about how to solve the second order differential below, where a is a constant: In the textbook, he solved it using the method of substitution i.e guessing the solution...
  24. V

    Satellite mechanics: linear and rotational momentum

    [This is a continuation of OP's thread here: https://www.physicsforums.com/threads/satellite-mechanics-linear-and-rotational-momentum.1046963/ ] satellite mechanics: linear and rotational momentum I'm trying to better understand classical mechanics, and came up with a question: Say we have a...
  25. Lotto

    Can two objects moving parallel relative to a ground meet?

    I think that yes but how to explain it when someone standing on a ground sees them moving paralell? If I move properly, I can see two cars moving paralell ralative to the ground crashing, while someone on the ground do not see them crashing. Is it consistent?
  26. Lotto

    What is the smallest value of angular displacement of the raft?

    What is meant by "the smallest value of angular displacement of the raft from its original position during one cycle"? I understand that I am supposed to solve this problem using torques of the crane and and of the boxes, but I am totally confused by that "smallest angular displacement". If it...
  27. V

    I Satellite mechanics: linear and rotational momentum

    satellite mechanics: linear and rotational momentum I'm trying to better understand classical mechanics, and came up with a question: Say we have a squared satellite weighting 100kg, 1 meter on each side. it has a thruster on it's side, shown in picture thruster quickly ejects 100g of propellant...
  28. A

    Classical A replacement for Mcauley's Classical mechanics

    Mcauley's "Classical mechanics: transformations, flows, integrable and chaotic dynamics" has a very interesting table of contents, and it has a philosophy of approaching Hamiltonian flows and chaos without using the formalism of modern differential geometry. Unfortunately, after reading the...
  29. S

    Distance travelled by a car considering only air friction?

    TL;DR Summary: Distance traveled by a car considering only air friction? How much distance would a 3-ton car travel if its initial speed was 17 km/h and we only take into account air's friction? (Assume that the car has an airfoil-like shape, so that the resistance against the air is very low)...
  30. luqman

    Coordinate Transformation (multivariable calculus)

    My Progress: I tried to perform the coordinate transformation by considering a general function ##f(\mathbf{k},\omega,\mathbf{R},T)## and see how its derivatives with respect all variable ##(\mathbf{k},\omega,\mathbf{R},T)## change: $$ \frac{\partial}{\partial\omega} f =...
  31. C

    I Variational Principles in Classical Mechanics (Douglas Cline)

    Hello, Has anyone read/heard about the textbook Variational Principles in Classical Mechanics, written by Douglas Cline? Any thoughts on whether I could use it as a replacement for Goldstein? Thank you!
  32. S

    I Water powered funicular with equal masses?

    I found a paper (https://www.researchgate.net/publication/312123871_Introducing_a_Modified_Water_Powered_Funicular_Technology_and_its_Prospective_In_Nepal) where the authors design a funicular system powered by water but with a modification from traditional systems where apparently the funicular...
  33. M

    B Irreversibility of Aristotle's law

    "Reversibility means that we never lose information, that at a fundamental level we can always retrodict the past as well as predict the future in the laws of physics". Susskind in his Theoretical minimum Lecture 2 describes about the laws which are true and which are not. He tells the law of...
  34. becks1

    Classical mechanics problem for a free particle

    Summary: The initial problem states: Consider a free particle of mass m moving in one space dimension with velocity v0. Its starting point is at x = x0 = 0 at time t = t0 = 0 and its end point is at x = x1 = v0t1 at time t = t1 > 0. and this info is to do the 3 problems written out. a)...
  35. Al-Layth

    I Comprehensive List of Mechanics Formulations

    beyond 1.) the Newtonian formulation 2.) The lagrangian formulation 3.) The Hamiltonian formulation What other formulations are there
  36. S

    I Receding movement of a stopped object in an accelerating universe?

    Imagine we attach an imaginary cosmological scale rope to an object that is very far away from us. Before attaching the string, the object would be receding from us due to spacetime expansion. After attaching it, tension would form in the string and we would eventually stop the object. After...
  37. P

    Maximum duration of Solar eclipses

    The result I get is 2 hours and 10 minutes. My reasoning is down here. But! Checking the map for the 2024 Solar eclipse, https://www.timeanddate.com/eclipse/map/2024-april-8, in many locations you can see a partial eclipse of over 2 hours 40 minutes. What is the main source of error here? Here...
  38. D

    Getting wrong answer in an (angular) impulse momentum problem

    I have tried this same approach three times and I got the same answer. I can't figure out what's wrong. Btw answer is 12mu/(3+cos2α) And yes, sorry for my shitty handwriting. If you can't understand the reasoning behind any step then please let me know.
  39. SaintRodriguez

    Please help me pick a topic for an essay about classical mechanics

    I was wondering if someone can telling me a topic about classical mechanics which I can write an essay. First I thought to write about Legendre transformation, but I guess that is very general. Also, if someone can tell me some tips to write an scientific essay I'll be so glad.
  40. bigmike94

    Prerequisites for John Taylor classical mechanics

    Inside the textbook, the prerequisites state first year mechanics and some differential equations, although it continues to say the differential equations can be learned as you’re working your way through the book, as differential equations were basically “invented” to be used for applied...
  41. H Ucar

    A Magnetic bound state in classical mechanics

    Seven years ago, I wanted to share and discuss my experiments results there but it was not possible since there was no published peer review paper yet and apparently not fulfilling forum requirements. Now we have such a publication, but still not sure the subject can be discussed here. Anyway...
  42. Physicsphysics

    I Understanding Classical Mechanics: Acceleration

    I'm reading once again through Landau-Lifchitz and I am stuck on the first page! I can't wrap my head around why we only need to define the coordinates and velocities to determine the acceleration? Surely if we only know those two in a single point in time, that's not enough to determine an...
  43. M

    B Why is KE not conserved when momentum is?

    Its clear in elastic collision that both KE and momentum is conserved. Bodies exchange their velocities. It is seen clearly in this video. There is no decrease in speed. Total KE is constant. But in an inelastic collision momentum is conserved again but not the KE. There is loss in KE (I guess...
  44. A

    What causes knots and stress when untwisting ropes?

    [Mentor Note -- thread moved from the schoolwork forums to GD as it seems like a more general question] Homework Statement:: Topoisomerases help in relieving strain in the DNA ahead of the replication fork caused by the untwisting of the double helix (Topoisomerases are enzymes that...
  45. AF Fardin

    Moment of inertia of a double physical pendulum

    I am having trouble to find the moment of inertia of the second rod! Is it related to the first rod?? At the beginning I thought It's not! But when took those as constant,the equation had become way much simpler and there is nothing about chaos! My approach is given below
  46. M

    B Does a body behave as a point mass even at rest?

    Hi, A body with center of mass behaves as a point mass when a force is applied. So when ##F_{ext}=0## then does it also behave as a point mass with ##a_{com}=0##, at rest. If yes, How can we prove this? (And can somebody please answer my other question I posted a week ago...
  47. M

    B K Energy & Momentum: Driving Force or Lost Heat?

    https://www.physicsforums.com/threads/conservation-of-momentum-and-loss-of-energy-in-inelastic-collisions.311037/post-2182192 If I understand correctly mathematically the momentum of the system remains unchanged but individual momentums decreases always. In an inelastic collision the momentum...
  48. bigmike94

    I Topics covered in John R Taylor Classical mechanics

    I can’t find the chapter list online, does anyone know what topics are covered in John Taylor’s classical mechanics? Would it be similar to what’s covered in Newtonian mechanics, but obviously more advanced. Cheers in advance 👍
  49. P

    Calculate tilt angle of a bar lifted via two ropes on fixed points

    Summary: How to calculate the equilibrium angle of a bar that is lifted on its two ends with ropes attached to fixed lifting points? Hello and good day all, First of all I would like to apologize in advance for my english, I am not a native speaker so some grammar errors may be left. My...
  50. Dario56

    I Why is it Impossible to Solve the Three Body Problem Analytically?

    Three (many) body problems where three or many bodies (particles) interact are impossible to solve analytically. First one appeared in classical mechanics where equations of motion of planets were tried to be found by applying Newton's 2nd law for system of planets and stars interacting via...
Back
Top