Classical mechanics Definition and 1000 Threads

Classical mechanics is a physical theory describing the motion of macroscopic objects, from projectiles to parts of machinery, and astronomical objects, such as spacecraft, planets, stars, and galaxies. For objects governed by classical mechanics, if the present state is known, it is possible to predict how it will move in the future (determinism), and how it has moved in the past (reversibility).
The earliest development of classical mechanics is often referred to as Newtonian mechanics. It consists of the physical concepts based on foundational works of Sir Isaac Newton, and the mathematical methods invented by Gottfried Wilhelm Leibniz, Joseph-Louis Lagrange, Leonhard Euler, and other contemporaries, in the 17th century to describe the motion of bodies under the influence of a system of forces. Later, more abstract methods were developed, leading to the reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. These advances, made predominantly in the 18th and 19th centuries, extend substantially beyond earlier works, particularly through their use of analytical mechanics. They are, with some modification, also used in all areas of modern physics.
Classical mechanics provides extremely accurate results when studying large objects that are not extremely massive and speeds not approaching the speed of light. When the objects being examined have about the size of an atom diameter, it becomes necessary to introduce the other major sub-field of mechanics: quantum mechanics. To describe velocities that are not small compared to the speed of light, special relativity is needed. In cases where objects become extremely massive, general relativity becomes applicable. However, a number of modern sources do include relativistic mechanics in classical physics, which in their view represents classical mechanics in its most developed and accurate form.

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  1. Z

    Classical Mechanics - Drag Force

    Homework Statement Suppose a block sliding on a slippery horizontal surface experiences a drag force F=-cv3/2 where c is a positive constant. At time t=0, the block is at position x=0 with initial positive velocity. Find the velocity and position as a function of time. Derive an expression for...
  2. A

    Electrical Breakdown/Avalanche of Air Classical Mechanics Collision Theory

    Homework Statement Electrical breakdown (e.g, lightning) is caused by an avalanche process. If a free electron gains enough energy between collisions to ionize the neutral molecules when they collide with them, then those two electrons will gain enough energy between collisions to ionize the...
  3. P

    Should I take QM 1 before completing Classical Mechanics?

    I just transferred to Georgia Tech from Georgia State and I'm registering for classes. I ave taken Intro Phys 1 and 2, and intro to modern physics. I have math up to DE. I will be taking Classical Mechanics this semester, and am wondering if it is a good idea to take QM before completing the...
  4. A

    Classical Mechanics: Fictitious Forces: Centrifugal, Coriolis, Transverse, etc.

    Homework Statement Figure is attached. In an amusement park ride called the hammer a large beam rotates in a ver- tical plane about a central pivot (see figure). Cages are attached to the end of the beam; these rotate independently. The riders are strapped to the walls of the cages. The...
  5. M

    First-Order Principles of Classical Mechanics

    My Physics teacher yesterday said something that gave me pause. He was talking about the necessity of clearly understanding the first-order principles of the science we study. Last semester I took Classical Mechanics (part 1 of the Introduction to Calculus-Based Physics at my college) with a...
  6. K

    What is the friction force required for a wheel to roll without slipping?

    A cord is wrapped around the inner drum of a wheel and pulled horizontally with a force of 200N. The wheel has a mass of 50 kg and a radius of gyration of 0.07 m. Let ms = 0.20 and mk = 0.15. (a) Determine the friction force, F at the wheel ground contact point assuming that the wheel rolls...
  7. F

    Classical Mechanics (Lagrangian)

    Homework Statement A ball is sitting on a frictionless seesaw with no inclination at the beginning, and a constant angular velocity \phi. Find the position of the ball as a function of timeHomework Equations L=T-V, T=(m\dot{}x2+m\dot{}y2)/2, V=mgyThe Attempt at a Solution The first problem I...
  8. R

    Classical Mechanics MatLab problem (oribtal motion)

    Hey guys, I've been fighting this problem all weekend with little avail. I only know a little Java, but we have this final project in MatLab, a program I don't really know.Homework Statement I need to compute the orbit of a comet using the Runge-Kutte, Euler and midpoint methods. The program...
  9. snoopies622

    How Does Dirac Challenge Classical Mechanics Assumptions in Quantum Theory?

    Dirac's Lectures on Quantum Mechanics begins with a big chapter on classical mechanics called "The Hamilton Method". Within the first ten pages he says, "Now in the usual dynamical theory, one makes the assumption that the momenta are independent functions of the velocities, but that...
  10. S

    Classical mechanics - Conservative system

    Could you please address the following? (1) For a conservative system, total energy (E = KE + PE) is a constant. It does not depend on time. Is it because of this time-independent nature that E is a constant of motion? (2) For a conservative system, the PE is a function of position...
  11. A

    Classical mechanics text recommendation

    I'm looking for a classical mechanics book that is heavily mathematical based, I've looked around a little however I'm lazy and don't want to buy a dud book. any recommendations would be great, thanks. (also i know there's 100000000000threads on text recom's however can't seem to find much ppl...
  12. I

    Which classical mechanics textbook is best for me?

    Which one would you recommend for me? Topics I'd like to have covered (most important ones): -Euler-Lagrange's equations -Lagrange's and Hamilton's approach to mechanics -Noether's theorem -KAM theorem -Bertrand's theorem -Poisson's brackets Plenty of examples and exercises would be...
  13. M

    Classical Mechanics collission particles

    Homework Statement particle of mass m1 collides with particle m2 at rest. The out come of the reaction were m3 and m4 which leave the collision at angles 3 and angle 4 withthe original path. find the energy of the reaction Q in terms of the masses and angles and p1 Homework Equations...
  14. L

    Classical Mechanics: Gravitation, SHM

    Homework Statement Let a particle slides in a straight smooth tube passing obliquely through the Earth. Assuming no friction and no rotational effects. Describe the motion. Find Frequency and Period. Homework Equations F = -GMm/r^2 The Attempt at a Solution Don't know how to...
  15. B

    When Will a Particle Reach the Force Center Under an Inverse Cubed Law?

    Homework Statement At t0 = 0 a particle of mass m is released from rest at x0 = b > 0 away from a fixed origin of force that attracts the particle according to the law: F=-k/x^3 where k >0 is a constant. At what time the particle will reach the force center x =0? Homework Equations I...
  16. M

    Classical Mechanics: Repelling Force and Motion Equations for F=ma

    Homework Statement Repelling force F=kx. What is the motion equation Homework Equations F=ma The Attempt at a Solution what I did so far, I found the equation of motion which is equal to x= sqrt(2E/K)Sin(wt+b), I am not sure about my answer. For the second part it is kind of tricky...
  17. A

    Instantaneous force propagation in classical mechanics

    I'm working my way (slowly) through Landau & Lif***z Classical Mechanics. I'm finally nearing the end of chapter one, and although I hit another stumbling block, I think I've got it now. If anyone has the time to check my reasoning, I'd be grateful. I will quote the passage that was confusing...
  18. Z

    Classical Mechanics (Taylor) 1.39

    So this was a textbook problem my professor did in lecture. I felt like I followed along with the logic as she went along, but after a few days and looking back it, I can't seem to recreate it genuinely. Homework Statement A ball is thrown with initial speed v0 up an inclined plane. The...
  19. Z

    Do I Need Classical Mechanics to Understand Quantum Mechanics?

    Do I need Classical mechanics and waves in order to understand Quantum mechanics? In order to learn quantum mechanics , do I need to know Classical mechanics and Waves or only linear algebra and calculus?
  20. F

    Courses What is the course Classical Mechanics ?

    What is the course "Classical Mechanics"? What is this course? Just a little harder version of calculus intro. to physics I? It's on the schedule as a sophmore course, and I have heard of a graduate course with the title too. What do you learn in it? I don't want to be retaught the very basics...
  21. M

    What is the acceleration at point A on a rotating merry go round?

    Ok so I have this circular merry go round and its rotating with a constant angular velocity \omega . There is a point A on the merry go round moving radially outward with a constant velocity V. Let the center of the circular merry go round be O. I want to find the acceleration of point A with...
  22. N

    Taking upper level classical mechanics early?

    I am currently in University Physics 1(calc-based intro to classical mechanics), and I talked with my adviser about taking Mechanics I(junior/senior level mechanics) course next semester. My adviser said it would probably be hard for me, but said he would let me "try it out." The reason I want...
  23. M

    Classical Physics: Is Research Still Ongoing?

    I'm a secondary school student as yet, wondering and want to know whether scientists still do researches on Classical Physics, or they have just known everything that they wanted to know about the Newtonian Physics In other words, are there still problems in Classical Physics the solutions of...
  24. C

    What are the central pillars of classical mechanics?

    From what I have understood, electrodynamics can be completely explained using classical mechanics, i.e. by plugging in the electromagnetic force and then predicting the dynamics using classicla mechanics. With classical mechanics being the more fundamental of these two classical theories, I...
  25. X

    Possible new reformulation of classical mechanics

    Let's say someone wanted to describe the motion of a 3D object in 3D space, for example maybe a ball in real space. Instead treating the ball as a 3D entity as a whole, how about just taking any point on the ball 1d point and just describe it's motion. In my example I'm assuming the point I...
  26. C

    Similar Classes? (Statics and Classical Mechanics)

    I'm leafing through "Engineering Mechanics - Statics" by Hibbeler, and it seems almost entirely a review of my Physics I class that was on Classical Mechanics. How is a class dedicated to Statics or Dynamics (both of which I will have to take) different from my classical mechanics class? It...
  27. L

    Quantum mechanics vs Classical mechanics

    Just a few questions that are really confusing me... 1. Where is the cut off boundary between the existence of Quantum mechanics and Classical mechanics, is there a specific point where classical takes over from quantum and if so where is that point? 2. Is the micro quantum world...
  28. S

    Solve Classical Mechanics Homework Statement

    Homework Statement http://img337.imageshack.us/img337/3014/classicalmechs.jpg I'm fine until showing that those 4 things are constants. Homework Equations dxj/dt=dh/dpj and dpj/dt=-dh/dxj The Attempt at a Solution I can't show they are constant, for example, can someone show...
  29. S

    Solving a differential equation in classical mechanics

    Homework Statement A particle of mass m is subject to a force F(v)=-bv^2 The initial position is zero, and initial speed is v_o Find x(t) The Attempt at a Solution for convenience's sake, define Q=-\frac{b}{m} therefore, {\ddot{x}}=Q{\dot{x}}^2 Let u=\dot{x} \dot{u}=Qu^2 then I just made...
  30. S

    Power series question involving classical mechanics

    Homework Statement A heavy weight is suspended by a cable and pulled to one side by a force F. How much force is required to hold the weight in equilibrium at a given distance x to one side. From classical mechanics, TcosX= W and TsinX=F. Find F/W as a power series of X(angle). Often in a...
  31. C

    Classical Mechanics Accelerated Frame/Rotation Problem

    Homework Statement Sally the physics student conducts the following experiment: There is a popular playground ride which is just a horizontal wooden disk free to rotate around a vertical axis. Sally hops onto the disk (spinning counter clock wise with angular velocity \omega ) with a bunch...
  32. C

    Classical Mechanics Accelerated Frame/Rotation Problem

    Homework Statement Sally the physics student conducts the following experiment: There is a popular playground ride which is just a horizontal wooden disk free to rotate around a vertical axis. Sally hops onto the disk (spinning counter clock wise with angular velocity \omega ) with a bunch of...
  33. P

    Classical Mechanics Video Lectures

    Hello, I wonder if you got any suggestions for classical mechanics video lectures? I don't mean freshman physics, but rather the course which includes the topics such as central body motion, lagrangian, hamiltonian, etc. (I guess it is considered as an upper level course on most schools)
  34. C

    Best Classical Mechanics Textbook

    Dear forum, I recently took an analytic mechanics course at UCLA in which the average grade on the first midterm was something like a 27 out of 80. The teacher was a brilliant man but unfortunately could not convey the material to the students. I don't think anyone felt as though they had...
  35. 1

    Classical mechanics - Time dependent Hamiltonian and Lagrangian

    Homework Statement A system with only one degree of freedom is described by the following Hamiltonian: H = \frac{p^2}{2A} + Bqpe^{-\alpha t} + \frac{AB}{2}q^2 e^{-\alpha t}(\alpha + Be^{-\alpha t}) + \frac{kq^2}{2} with A, B, alpha and k constants. a) Find a Lagrangian...
  36. fluidistic

    Classical mechanics, initial conditions question

    I just started CM (I had 2 classes until now) and the professor said that if you know the position and velocity of say all the particles, then you know how the system will evolve. This, I already read and knew. I've probably a common question so feel free to redirect me to any similar...
  37. P

    How does classical mechanics change if motion was not infinitely differentiable?

    Many "theoretical mechanicians" seem to awesome that motion is a {C^\infty } function(at least that is how I learned it). However, it seems like the postulates of Newtonian/Lagrangian/Hamiltonian/Vakonomic mechanics seem to "work" in the general case where only the motion is a {C^2}(ie the...
  38. M

    How Can Viscous Drag Affect the Velocity of a Sliding Block?

    Homework Statement heres a problem i working on a block slides on a horizontal surface which has been lubricated with a heavy oil such that the block experiences a viscous drag resistance in the opposite direction to the velocity and that varies with speed according to: F\left( v\right)...
  39. D

    Classical Mechanics: Textbook Recs & Study Tips

    I can already tell this semester is going to be a rough one. With two weeks until the semester begins, I've been attempting to work through the notes for my classical mechanics course (lagrangian & hamiltonian mechanics). Wow. Really dense stuff. I'm having a pretty difficult time following the...
  40. B

    Newton's third breakage in Goldstein's classical mechanics

    Newton's third breakage in Goldstein's "classical mechanics" I was reading Goldstein's Classical Mechanics vol.2 to brush up, and didn't get far before I got stuck. The book warns that both the weak an strong forms of the action/reaction principle can be broken when forces predicted by the...
  41. H

    Classical mechanics problem book

    I'm on first semester, having classic mechanics cource and i need some good problem book with problems, with to be solved require more than just knowing forumula.
  42. P

    Reconciling quantum with classical mechanics

    Homework Statement The pendulum of a grandfather clock has a period of 1 s and makes excursions of 3 cm either side of dead centre. Given that the bob weighs 0.2 kg, around what value of n would you expect its non-negligible quantum amplitudes to cluster? The Attempt at a Solution I...
  43. W

    Is research still being done in Classical Mechanics? (and another question)

    ^ topic It just seems Classical Mechanics seems to be the most "complete" sub-field of Physics but I was just wondering. Also, I have just finished taking my Classical Mechanics I class at my university (and I want to give a thank you to the forum again for helping me) and to be honest...
  44. S

    Upper Division Classical Mechanics for Dummies?

    Well, I took a junior level classical mechanics course. We used Marion (the 4th edition). I guess I’m retarded or something because it just didn’t make a whole lot of sense to me… My professor didn’t help much either (most students “got him” but he just didn’t mesh with my learning style)…...
  45. P

    Project Ideas for Classical Mechanics

    I am enrolled in a Classical mechanics course. The course covers topics such as Euler angles, Lagrange equations, change of reference frame, two body problem, rigid body dynamics, etc. We're using the Marion and Thornton text. We were given a final project. We can either apply these concepts...
  46. S

    Self Study book for Classical Mechanics?

    I'm looking to find a cheap and short intro to the minimum knowledge of Classical Mechanics(Hamilton/Lagrange formulations) you need to know to understand properly Quantum Mechanics. Any recommendations? I'm not worried about it being too rigorous or in depth since I will take a full class in...
  47. C

    Solving Classical Mechanics #3d - Momentum p in Jaccobi Function

    Homework Statement The problem is number 3d in the following file: http://phstudy.technion.ac.il/~wn114101/hw/wn2010_hw06.pdf The Attempt at a Solution I think the difference comes from the using of the momentum p. In the Jaccobi function, we use only coordinate x and its...
  48. S

    Classical Mechanics, clyinder inside a cylinder.

    b]1. Homework Statement [/b] A cylinder (solid) of radius a rolls inside a fixed hollow cylinder of radius 4a; inside a homogenous gravity field. Find, langragian using the rolling angle of the little cylidner as a generalized co-ord. angular frequency of small oscilalations about...
  49. P

    Advise on how to study (and catch up) in Classical Mechanics

    Hello all, Doing this week's problem set, I realized that I have become totally lost in my classical mechanics class. Part of the problem is that my other classes are also very time demanding that I end up putting classical mechanics off because it is so dry (for me at least). The other...
  50. J

    Which textbook is the best for learning classical mechanics?

    https://www.amazon.com/dp/189138922X/?tag=pfamazon01-20 Has anyone ever read this book? It looks like a bargain, good reviews, low price. What do you think of it? Is it a good mathematically oriented physics book?
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