What is Classical mechanics: Definition and 1000 Discussions

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.

View More On Wikipedia.org
Recent contents Top users
  1. Greg Bernhardt

    Mathematical Methods of Classical Mechanics by V.I. Arnol'd

    Author: V.I. Arnol'd (Author), K. Vogtmann (Translator), A. Weinstein (Translator) Title: Mathematical Methods of Classical Mechanics Amazon Link: https://www.amazon.com/dp/1441930876/?tag=pfamazon01-20 Prerequisities: Contents:
  2. C

    Classical mechanics, Hamiltonian formalism, change of variables

    Homework Statement This problem has to do with a canonical transformation and Hamiltonian formalism. Below is my attempt at solving it, but I am not too sure about it. Please help! Let \theta be some parameter. And X_1=x_1\cos \theta-y_2\sin\theta\\ Y_1=y_1\cos \theta+x_2\sin\theta\\...
  3. B

    Physics Dilemma: I want to be a physicist, but I'm mediocre in classical mechanics

    Hi everyone. I'm having a little crisis here. I'm really really good in math (I'm doing calculus right now, and it's a breeze), but classical mechanics are giving me a hard time. I'm also doing general chemistry right now and I find it fun and easy as well. Basically, the more abstract...
  4. A

    A Quest to Perfectly Understand Classical Mechanics

    Hi, I'm currently a sophomore at college trying to perfect his understanding of classical mechanics. I finished Taylor's book a while ago, but now once again realized that I still don't understand mechanics all that well. So, I'm going to start from scratch. And dig deep, questioning...
  5. G

    Additional problems in Classical Mechanics

    Hello, Since I cannot post this in the "Learning Materials" forum, I thought I'll just post it here. I am a first year Physics/Biology major, and I am currently studying a course in classical mechanics. My problem is that I do not seem to find high level problems in mechanics anywhere online...
  6. B

    Classical Mechanics: Minimization of geodesic on a sphere

    Homework Statement Use the result (6.41) of Problem 6.1 to prove that the geodesic (shortest path) between two given points on a sphere is a great circle. [Hint: The integrand f(ψ,ψ',θ) in (6.41) is independent of ψ, so the Euler-Lagrange equation reduces to ∂f/ψ' = c, a constant. This gives...
  7. A

    Under what conditions does quantum mechanics reduce to classical mechanics?

    Homework Statement "At 310K thermal energy kT=4.28x(10^-21). Use the equation you derived above (which I worked out to be E=(n²h²)/(8mL²) )to determine under which conditions quantum mechanics reduces to classical mechanics." The hint was that "you need to find the value of mL² for which change...
  8. N

    Testing How to Study for a Classical Mechanics Exam?

    I am writing to ask you for advice on how I should go about studying for the upcoming Classical Mechanics exam. I would only be satisfied to get an A, nothing less, so I am willing to work hard. Although I realize that preparing for the midterm exam begins when the semester starts, I don't feel...
  9. C

    Classical Mechanics, Double Star, Find the ratio of the masses

    Homework Statement The two components of a double star are observed to move in circles of radii r1 and r2. What is the ratio of their masses? (Hint: Write down their accelerations in terms of the angular velocity of rotation, ω.) Homework Equations Newton's 2nd law? law of...
  10. F

    Classical Mechanics - Learning Guidance

    Hi I am looking for some advice. Would like a bit of guidance into any good resources and specific maths/physics disciplines to study in relation to what I would term 'sports classical mechanics'. Not looking for any university or specific course references at the moment unless you think...
  11. M

    Equation 1.51 in Goldstein's 3rd edition of Classical Mechanics

    I am trying to self-study some physics, and have gotten a little stuck in one of Goldstein's derivations. The dot-notation is still confusing to me. Equation 1.51 in Goldstein states that \frac{\partial \vec{v_i}}{\partial \dot{q_j}} = \frac{\partial \vec{r_i}}{q_j} I do not understand how...
  12. S

    Goldstein classical mechanics discrepancy?

    Homework Statement In Goldstein's text, he discusses conservative fields and then states that "friction or dissipative forces are never conservative since F dot ds is always positive." From what I recall, most frictional interactions occur in directions opposite the displacement, and would...
  13. S

    Super-hard differential equation in classical mechanics problem

    Homework Statement A particle of mass m moves in the following (repulsive) field U(x) = α/x², α > 0, with α a constant parameter. Determine the (unique) trajectory of the particle, x(t), corresponding to the initial conditions of the form x(t0) = x0 > 0, x'(t0) =...
  14. S

    Classical Mechanics: Forces on two cylinders

    Homework Statement Two identical, uniform and rigid cylinders, each of radius a and mass m, are laid horizontally at rest inside a rigid box of width w. There is no friction acting at any of the four contacts. i) Draw a diagram for each cylinder showing the forces acting on it alone...
  15. V

    Research Papers in classical mechanics

    Please tell me a website where I can find latest research papers in classical mechanics.
  16. R

    What are some recommended books for graduate level classical mechanics studies?

    I want a good book on classical mechanics - one that would be considered to be a graduate level text. The only Physics courses I have taken are the two standard intro physics courses taught at what seems to be every university, and a course in Computational Physics. My (relevant) math...
  17. X

    Classical mechanics, simple pendulum

    Homework Statement See attachment "question" Homework Equations The Attempt at a Solution See attachment "work" I did the work for (1) and (2). I end up with two equations: the first is the tension T, the second is the angular acceleration. I'm not so sure if I made any...
  18. wolfspirit

    Equations in Classical Mechanics

    hi i am a bit confused watching lectures and reeding books i quite often come across dx/dt and i don't know what the "d" is. the full equation is F=ma which was rewritable as F=m*dx/dt many thanks for any help
  19. N

    Exploring Frictionless Climbing on a Conical Mountain: Cheap vs Deluxe Lassos

    So I've ordered Taylor's book in classical mechanics and I need some advice. My plan is to solve as many problems as I can in classical mechanics, since it seems that the type of logical thinking that is needed in classical mechanics will surface time and time again in following physics...
  20. P

    Electron Magnetic Moment's Difference From Classical Mechanics

    I was reading the Wikipedia article on Electron magnetic dipole moments and it mentioned that the "g-factor" is need in determining the magnetic moment of an electron because it varies by approximately two from the prediction of classical mechanics. Why exactly does this discrepancy occur?
  21. M

    Orbits for classical mechanics

    Find the orbits for the m mass under the F(r)=-A/r^2+B/r^3 . Where A>0 and B is positive or negative. Friends, please help me for homework
  22. D

    Is classical mechanics needed before E&M (Griffiths)

    This summer I plan to self study quite a bit and want to learn as much as I can. I'm an EE major and have taken Calc 1-3, and DiffyQ/Linear algebra as well as intro physics classes. I will be taking classical mechanics in Spring 2013 but wanted to dive into Griffiths E&M book this summer. Is...
  23. B

    Testing Navigating a Classical Mechanics Final with 11 Hours to Prepare

    Ok, so I feel really bummed out even having to ask this question, but in all seriousness: I have a classical mechanics final in 11 hours. It's upper division CM not like first year stuff. Anyway, I'm decently prepared. I mean, if I take it now I will certainly pass. But I want the best...
  24. S

    How Does Angular Momentum Affect the Velocity of a Disc on a Frictionless Table?

    Homework Statement A disc of mass M, which may be considered to be a point mass, is placed on a frictionless horizontal table. A massless string is fastened to the disc and is passed through a small hole at the centre of the table. The lower end of the string is tied to the end of a flexible...
  25. P

    Calculating Time for an Airplane to Come to Rest Using Classical Mechanics

    Homework Statement An airplane touches down at a speed of 100m/s. It travels 1000 metres along the runway while deceleration at a constant rate before coming to rest. How long did it take the airplane to come to rest on the runway? Xi=0m/s Xf=1000m Vix=100m/s Homework Equations...
  26. S

    Difficult Problems in Classical Mechanics

    My professor for classical mechanics has asked that we find some difficult problems in classical and solve them. My first thought was to look through my book for hard problems. However, we are using a free PDF that is rather lackluster when it comes to homework problems. Almost all of the...
  27. C

    Classical Mechanics for Mathematician

    Hi! I am looking for suitable ways to learn mechanics in mathematician's perspective. I went through: - multivariable calculus from Spivak, - real analysis from Pugh, - differential equations from Hirsh/Smale/Devaney (mostly focusing on linear system, existence & uniqueness, nonlinear...
  28. M

    Some Good Exercise Book For Classical Mechanics.

    I need a good book, or in other words a book and it's solution manual if available on line - in classical physics. Some Lagrange, Hamiltonian exercises, with good explanation. Thanks in advance.
  29. E

    Advanced undergrad/grad book for classical mechanics as macro limit of QM

    Hi folks. I'm wondering who does a good job of explaining this limit, preferably with a good set of examples. It doesn't need to be too basic, but it'd be nice if it went through the phase space stuff a little (I get the impression that my grad prof didn't do a great job with some details based...
  30. P

    Proof using mainly classical mechanics

    Hey, http://img822.imageshack.us/img822/407/25944209.jpg \begin{align} & \frac{m{{v}^{2}}}{r}=\frac{Z{{e}^{2}}}{4\pi {{\varepsilon }_{0}}{{r}^{2}}} \\ & L=\frac{Z{{e}^{2}}}{4\pi {{\varepsilon }_{0}}v} \\ \end{align} and I know by using the v derived using Bohr's equations it will give...
  31. C

    What mindset is required for Classical Mechanics

    I hope this is in the right sub forum, but my question is simple. What type of mindset is required to complete problems in a 2nd year classical mechanics course. Comparing a typical classical mechanics problem to a 1st year physics problem, they are both completely different. I find that a...
  32. Z

    Determinism of classical mechanics

    Is classical mechanics deterministic? If so, please explain this. Suppose we collide two bodies with each other. Assuming they are point particles and using conservation of energy and momentum this gives us a set of equations. Unfortunately these aren't enough to predict their...
  33. O

    Classical Mechanics: Lagrangian for pendulum with oscillating support

    Homework Statement Greetings! This is an example problem at the end of Chapter 1 in Mechanics (Landau): A simple pendulum of mass m whose point of support oscillates horizontally in the plane of motion of the pendulum according to the law x=acos(\gamma t) . Find the Lagrangian...
  34. jinksys

    Classical Mechanics - Box sliding down a slope

    I'm on pg 56 of Thorton's Classical Dynamics book and I see this: Imgur Link Two questions: 1) Where does the 2 go on the second to last equation. 2) Why v0^2 and not v0 on the integral?
  35. M

    Classical Mechanics Acceleration under force F=-K/x^2

    Here's a classical mechanics problem I'm having some trouble with: A particle of mass m moves on the positive x-axis under the influence of a force F=-K/x^2, where K is a positive constant. The particle is released from rest at x=R at time 0. Find the velocity as a function of x as it...
  36. T

    How long does it take for a plane to come to a stop in an emergency landing?

    Homework Statement This is a problem from K & K, but I changed it very slightly. A light plane weighing 2,500 lb makes an emergency landing on a short runway. With its engine off, it lands on the runway at 120 ft/s. A hook on the plane snags a cable attached to a 250 lb sandbag and drags...
  37. fluidistic

    Classical mechanics, motion of a particle over a helix

    Homework Statement I'm doing past a past exam (2003) and I'm stuck on the first exercise. Here it is: Consider a helix centered in the z-axis, of radius R and fixed step a, given in cylindrical coordinates by z=\frac{a\theta }{2 \pi }, r=R. A particle of mass m slides without rolling over the...
  38. T

    Best Classical Mechanics textbook for undergrad level

    What would be your go-to textbook for Classical Mechanics at the undergraduate level? It must also cover the Lagrangian and Hamiltonian formulation. My school uses "Analytical Mechanics" by Fowles & Cassiday but I find it not very complete and doesn't cover all topics. I've also read parts...
  39. J

    Classical Mechanics: Simple harmonic oscillator problem

    Homework Statement A simple harmonic oscillator with mass m = 1/2 and k = 2 is initially at the point x = √3 when it is projected towards the origin with speed 2. Find the equation of motion describing x(t). Homework Equations x=Asin(ωt+θ) The Attempt at a Solution At t=0...
  40. J

    Classical Mechanics: Finding force, equilibrium points, turning points

    Classical Mechanics: Finding force, equilibrium points, turning points... Homework Statement The potential energy between two atoms in a molecule is U(x) = −1/x^6 +1/x^12 Assume that one of the atoms is very heavy and remains at the origin at rest, and the other (m = 1) is much less...
  41. I

    Spontaneous disintegration in classical mechanics

    Could someone demonstrate to me how in Landau's Mechanics book, he gets from equation (16.5) tan θ = (v_0 sin θ_0) / (v_0 cos θ_0 + V) to equation (16.6) cos θ_0 = -(V/v_0) sin^2 θ ± cos θ √[1 - (V/v_0)^2 sin^2 θ] I am using the quadratic formula, and the first term on the right...
  42. Y

    Classical Mechanics Kleppner Problem

    Homework Statement An Instrument carrying a projectile accidentally explodes at he top of its trajectory.The horizontal distance b/w the launch point and the point of explosion is L. The projectile breaks into 2 pieces which fly horizontally apart. The larger piece has three time the mass of...
  43. I

    A problem regarding to Lagrangian in Classical Mechanics

    Homework Statement I have a problem regarding to lagrangian. If L is a Lagrangian for a system of n degrees of freedom satisfying Lagrange's equations, show by direct substitution that L' = L + \frac{d F(q_1,...,q_n,t)}{d t} also satisfies Lagrange's equations where F is any ARBITRARY BUT...
  44. TurtleMeister

    Active versus passive mass in classical mechanics

    I like your explanation, and I agree. However, why does it not work for the case of gravity? To be more specific, I'm talking about the mainstream classical justification for the equivalence principle as it applies to active gravitational mass. Let me give an analogy that applies to the OPs...
  45. O

    Best online resource for classical mechanics

    I'm learning mechanics right now via an extension course. In the absence of an "on-demand" teacher I've found multiple textbooks and online resources to be useful. When I studied calculus, Paul's online calculus notes (http://tutorial.math.lamar.edu/Classes/CalcII/CalcII.aspx) were a great...
  46. I

    Classical mechanics - mass/spring attached to moving support

    Homework Statement A mass, m, is attached to a support by a spring with spring constant, k. The mass is hanging down from the spring, so there is a gravitational force on the mass as well. Neglect any resistive or frictional force. The support is then oscillated with an amplitude of A and...
  47. N

    Contemporary applications of Classical Mechanics?

    Hey guys, First time posting. I was thinking of starting an extra credit paper for my Physics 1A course, and was wondering if anybody could think of any noteworthy and recent applications of classical mechanics that I could do some research on. I was thinking of maybe pursuing dark matter as...
  48. D

    Configuration Space In Classical Mechanics: Definition

    Hi, I'm a bit confused wit the concept Configuration Space. First, the professor defined generalised coordinates as such: U got a system of n particles, each particle has 3 coordinates(x,y,z), so u got 3n degrees of freedom. If the system has k holonomic constraints, u got 3n-k degrees...
  49. C

    Messed up classical mechanics problem:

    This is really simple but I can't figure it out. I was on a bus when I thought of this: Say I'm sitting in the back of a bus which is traveling on a flat surface, and accelerating with a constant acceleration (forward). Now I get up from my seat in the back and make my way to the front of the...
  50. F

    Classical Mechanics, Coupled Harmonic motion

    Homework Statement Set up the equations of motion for the system shown in Fig. 4.16. The relaxed lengths of the two springs are l1, l2 . Separate the problem into two problems, one involving the motion of the center of mass, and the other involving the "internal motion" described by the two...
Back
Top