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. H

    Frictionless Disk Supported by Massless String

    In the following diagram, a frictionless disc is supported by a massless string. This problem was given by the author of a book, and a solution was given to some questions that were asked about this diagram. One thing the author said in one of the solutions, was that the tension in the string...
  2. B

    Classical Mechanics Textbooks: A Must-Have for Physics Students

    I'm sophomore in physics looking for best free books for classical mechanics and for vibrations and waves. Anyone with references pleaseThank you
  3. PrathameshR

    Use of Lagrange's equations in classical mechanics

    I have been studying classical mechanics for a while from Goldstein book and can't go ahead of the following derivation. I understand the method of Lagrange's multipliers for getting extrima of a function subjected to equality constraints but can't understand it's relevance here because in that...
  4. I

    Bead Sliding on Rotating Rod after Motor is Turned Off

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  5. Alexander350

    B Where does this equation for stationary points come from?

    In the Classical Mechanics volume of The Theoretical Minimum, he writes a shorthand equation for a small change in a function. Please could someone explain exactly what it means and where it comes from?
  6. T

    B Why will an object in space continue moving foever?

    Why object in the space will continue moving foever if the object is in dynamic equilibrium?
  7. senatorarmstrong

    Courses Preparing for Classical Mechanics: Tips for Success

    Hello PF, I am taking classical mechanics this fall and I am horrified. I am just not sure if I have the mathematics background for the class. I am still finishing differential equations (about half way done) and I am almost done with calculus 3. The pre-requisite for the class is DE...
  8. J

    I How to model Solar System formation accurately and realistically

    I've been working on a crude N-body simulator which allows N bodies of equal masses to interact gravitationally in 2 dimensions. My goal is to model the formation of Solar System. Each body is modeled as a circle with a radius as a function of its mass, in such a way that all bodies have the...
  9. C

    Determining Acceleration of Hinge in a Beam and Hinge Structure

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  10. R

    I Amplitudes of Fourier expansion of a vector as the generalized coordinates

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  11. E

    Classical Mechanics, MIT 8.01 -- Useful learning resource?

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  12. R

    A The Lagrangian a function of 'v' only and proving v is constant

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  13. T

    B What is the force acting on a seesaw?

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  14. C

    Difficulty with Mathematical Methods of Classical Mechanics

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  15. Salvador_

    Classical mechanics differential equation F(x) = -kx

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  16. T

    Intro Physics Is Kleppner Mechanics Suitable for Self-Study After High School?

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  17. V

    Continuum mechanics in physics education

    I came across this article about the near absence of continuum mechanics in university-level physics education: http://www.troian.caltech.edu/papers/Gollub_PhysToday_Dec03.pdf I have wondered this issue myself: why is continuum mechanics mainly studied by engineers rather than physicists, even...
  18. J

    Classical mechanics: Jacobi variational principle

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  19. A

    About centripetal acceleration

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  20. unseeingdog

    B Coefficient of Restitution in x and y

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  21. Val Antthony

    Classical Which classical mechanics book has better content?

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  22. Dimani4

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  23. H

    Calculating the equations of motion for particle in parabola

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  24. A

    Tension on the rope (classical mechanics problem)

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  25. C

    Classical Which Classical Mechanics book to get?

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  26. G

    Looking for a Classical Mechanics Book by Goldstein?

    I need a book written just on the style of Classical Mechanics by Goldstein. I don't remember the book name and author but it is just the copy of the book Classical Mechanics by Goldstein. Please guide.
  27. R

    Calculating the moment of inertia of a solid sphere

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  28. R

    Simple Harmonic Oscillator behaviour when a potential term is added

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  29. N

    How weight affects surface bending over time

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  30. benny91xp

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  31. S

    A One Hamiltonian formalism query - source is Goldstein's book

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  32. S

    Rolling ball and generalized co-ordinates

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  33. N

    I Classical v. quantum dynamics: Is spin the key difference?

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  34. Mind----Blown

    Significance of terms of acceleration in polar coordinates

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  35. 1

    Help finding the vibrational frequencies and normal modes

    Homework Statement Let's say that I have a potential ##U(x) = \beta (x^2-\alpha ^2)^2## with minima at ##x=\pm \alpha##. I need to find the normal modes and vibrational frequencies. How do I do this? Homework Equations ##U(x) = \beta (x^2-\alpha ^2)^2## ##F=-kx=-m\omega ^2 x## ##\omega =...
  36. T

    Rigid body orientation using Euler angles confusion

    Hello, Homework Statement I'm given the following exercise: "A rod with neglected thickness exists. What is the relation between the α,β angles to Euler angles of orientation? α is defined as the angle between the rod and its projection on the XY plane. β is defined as the angle between the...
  37. zwierz

    A Classical Mechanics challenge for fun

    I composed a problem and propose it here. I know the solution so it just for fun of the participants. There is a cylindrical bobbin of radius ##r##; the bobbin rotates about its central axis with angular velocity ##\omega=const>0##. An inextensible weightless string is coiled around the...
  38. J

    I Difference between statistical and dynamical properties

    Hi All, What are the main differences between statistical and dynamics properties in physics? Could you please explain the difference for problems in both classical and quantum mechanics. For instance, path integral molecular dynamics is supposed to give statistical properties of a quantum...
  39. L

    Why is Newton's equation of motion invariant to time reversal

    Is there any deep reason behind this? per example the principle of least action or something else?
  40. L

    I A question about Noether theorem

    How can I derive that the work of a force perpendicular to velocity is always zero from the theorem of Noether? I have heard that there is a relation between these two but in Google I found nothing. Thank you very much
  41. smodak

    Classical Found a great resource on Theoretical Mechanics (free)

    Classical mechanics: a minimal standard course by Sergei Winitzki. It is not probably going to help you if you already did not know the subject but is a great refresher nonetheless. He also includes a differential equations refresher that I found invaluable. Looks like he has a ton of other...
  42. T

    Classical mechanics electrostatics and charges

    Homework Statement hi i was doing a practice physics junior olympiad paper when i got stuck in question 11 in this link [/B] https://www.scribd.com/document/244111815/SJPO-2013-Special-Round-pdf Edit by moderator: Inserted relevant extract of the PDF so that helpers do not have to...
  43. durant35

    I Many Worlds vs Classical Mechanics

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  44. L

    Derivation of Rocket Equation Using Relative Velocity

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  45. Xell

    Classical What is a good, basic classical mechanics textbook?

    I would like one that is not very mathematically intense, and not to advanced, thanks for any replies.
  46. E

    Relative Acceleration - Particle and Wedge

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  47. Mikkel

    Classical Mechanics - Find angular velocity of two rods

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  48. Elvis 123456789

    A rope falling off an inclined plane

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  49. yesudeep

    How Does Physics Impact Tennis Performance?

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  50. J

    I Connection between Foucault pendulum and parallel transport

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