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. R

    Lagrangian of a pendulum system

    Homework Statement A long light inflexible rod is free to rotate in a vertical plane about a fixed point O. A particle of mass m is fixed to the rod at a point P a distance ℓ from O. A second particle of mass m is free to move along the rod, and is attracted to the point O by an elastic force...
  2. S

    Identifying conserved quantities using Noether's theorem

    I've been asked to find the conserved quantities of the following potentials: i) U(r) = U(x^2), ii) U(r) = U(x^2 + y^2) and iii) U(r) = U(x^2 + y^2 + z^2). For the first one, there is no time dependence or dependence on the y or z coordinate therefore energy is conserved and linear momentum in...
  3. person_random_normal

    Classical Mechanics: Torque, Angular Momentum & Origins

    In classical physics , specifically in rotational mechanics we have concepts of torque , angular momentum and their extensions. We widely use them in problem solving but how were they defined , what was the basis of their definition , was all that purely experimental and most importantly who did...
  4. M

    How to solve for first integrals of motion

    Homework Statement A point particle is moving in a field, where its potential energy is U=-α/r. Find first motion integrals. Homework Equations How to derive it The Attempt at a Solution I only figured out that all of this is related to the conservation of energy, but i don't know even the...
  5. S

    Buckingham-Pi for "algorithmic" non-dimensionalization

    I would like to use the Buckingham-Pi theorem in order to "algorithmify" non-dimensionalization of existing equations. I can get things to work for very simple problems, but am running into issues with a harder example. I posted my question on physics.stackexchange.com the day before yesterday...
  6. M

    Unsolved Scientific Problems in Classical Mechanics

    Hallo Everyone, What are the most important unsolved problems in Classical Mechanics especially related to mechanics of rigid body mechanics, deformable-body mechanics and, fluid mechanics.
  7. B

    Classical mechanics changing mass

    hey there, i need your help, I am a student in physics and electricity engineering, and i have a bit of a problem with the changing mass materiel, well in first look he's pretty easy but i want to learn how to create my own equations and I am never getting the same result. so ill be glad if...
  8. DrPapper

    Classical Fundamental Principles of Classical Mechanics - Kai S. Lam

    Hello all, I'm currently taking an upper undergraduate two part Mechanics course using the above mentioned book by its author. He's a great professor and I was wondering if anyone else has checked out this book? It's very math heavy and I'm struggling with some of the language since I haven't...
  9. pitbull

    Website for Classical Mechanics

    Do you guys know of any website that has solved problems of Lagrange Mechanics?
  10. A

    Classical Classical mechanics book recommendations please

    I was wondering if anyone could suggest any books that would describe and explain basic and some more advanced mechanics with a reasonable amount of mathematical content? Cheers
  11. pitbull

    Optimizing the Pivot Point for a Uniform Bar's Frequency of Oscillation

    Homework Statement Given a uniform bar of length L, which point should you hang it from (between 0 and L) so that you get maximum frequency for small oscillations? Homework Equations ... The Attempt at a Solution It seems like a basic problem, but I don´t know how to start. Could you guys...
  12. Bleakfacade

    Classical Mechanics by Arnold Sommerfeld- review

    I am trying to dig deep into classical mechanics. Among many suggestions, this was an odd one to me. I know of Arnold Sommerfeld and his work, but I have not read any of his works(books, papers, .etc). I tried to find reviews of this book online to no avail. If there are people who have read the...
  13. S

    Classical Recommedation for Classical Mechanics book

    There will be a competition in classical mechanics and I need a good book to prepare. The competiton was also held last year and i ended up thir, so I dear to say that I know classical mechanics very well. The competition will include kinematics, dynamics, law of conservation of energy, Newton's...
  14. A

    Classical Need a reference for Mechanics book

    I need a reference book to read the following topics- a) Generalized coordinates; b) D'Alembert's principle and Lagrange's equations; c)Hamilton equations; d) Motion of rigid bodies in two dimensions. The topics need to be covered only at graduation level. Thanking you in anticipation.
  15. S

    If Faraday invented field concept, how did Newton find g?

    This is Newton's law of universal gravitation. $$F=G\frac{m_1.m_2}{r^2}$$ Gravitational field $$g$$ is derived from this formula $$g=G\frac{m_1}{r^2}$$ This is named gravitational "field" strength. If Newton knew nothing about "field concept" and formulated his formula in the form of "action...
  16. snatchingthepi

    Need a new classical mechanics book

    I've finished my institution's sequence on classical mechanics and am wanting to keep reading the subject. Does anyone have a standard suggestion after Fowles/Cassiday "Analytical Mechanics"? We covered almost the entire book except for the very last chapter and a few sections on oscillations...
  17. V

    Ionospheric electron under non-uniform acceleration

    In 'Introduction to Mechanics' by Kleppner and Kolenkow...motion of ionospheric electron under non-uniform acceleration is x = (a0/w)t - (a0/w^2)sin wt...my question is when there is non-uniform acceleration, it makes sense to have sinusoidal part in the motion...but how come there is uniform...
  18. G

    Rod-Spring System Homework: Verifying Parts a) & b)

    Homework Statement I'm really looking for a verification on parts a) and b), but I'll add what I did with part c) without going to into too much detail. I'm posting this question mainly due to part d). I feel that I have every part before this right, but I'm not getting any symmetric...
  19. S

    Intuition behind Hamilton's Variational Principle

    Background: I am an upper level undergraduate physics student who just completed a course in classical mechanics, concluding with Lagrangian Mechanics and Hamilton's Variational Principle. My professor gave a lecture on the material, and his explanation struck me as a truism. Essentially, he...
  20. V

    What Should I learn before reading this book on Classical Mechanics?

    I am about to read the book Classical Mechanics by Herbert Goldstein. The prerequisites that it says in the book are advanced calculus and vector analysis. Would that mean multivariable calculus? Also there are a lot of things about transformation matrices and tensors. Would I need to review...
  21. T

    Classical Mechanics - Potential Energy Function

    Homework Statement The potential energy function of a particle of mass m is V(x) = cx/(x2+a2), where c and a are positive constants. Qualitatively sketch V as a function of x. Find two equilibrium points: identify which is a position of stable equilibrium, and find the period of small...
  22. E

    Classical Mechanics: Coriolis Effect Problem

    Homework Statement A bird of mass 2 kg is flying at 10 m/s in latitude of 60° N, heading due East. Find the horizontal and vertical components of the Coriolis force acting on it. Homework Equations The Coriolis Force, F = 2mw∧v. Where ∧ shows the cross product between angular frequency...
  23. Strilanc

    Distinguishing Special Relativity from Classical Mechanics

    I was recently reading the strange world of classical mechanics. It prompted me to calculate some round trip times for things moving near the speed of light (classically, with an aether). I found that the predictions it makes are awfully similar to relativity, and I can't think of an experiment...
  24. S

    How to study Theoretical Mechanics?

    I know Single variable Calculus and I have a basic understanding of multivariable calculus. I also happen to know basic linear algebra. What are the mathematical pre-requisites needed in order to self-study theoretical mechanics? I'm planning to take this course...
  25. Erland

    Two errors about rotations in Goldstein's "Classical Mechanics"

    Classical Mechanics by Herbert Goldstein is one of the most used textbooks on this subject, perhaps the most used one. However, I found a couple of errors in Section 4.9 (in 3rd ed, written with Charles Poole and John Safko) about rotations. First, at p. 172, the angular velocity vector ω is...
  26. V

    Mathematical Considerations of Spacetime in Classical Mechanics

    When studying the motion of particles in space, what are the mathematical considerations that have to made of spacetime? Could I say there exists a bijection between spacetime and ##\mathbb{R}^4##? Is the topology under consideration the usual product topology of ##\mathbb{R}^4##? Are there any...
  27. thegreengineer

    Clarifying Hooke's Law: Understanding the Formula and When to Use the Negative

    Well, I know that Hooke's law establishes that the force applied on a spring is proportional to the displacement. However, I've got a little bit confused about the formula. My textbook manages the formula as the following: F=-kx Whereas some websites manage it as this: F=kx I still don't...
  28. R

    Precession of relativistic orbit in pure inverse-square force

    PROBLEM: Show that Special Relativity predicts a precession of π(GMm/cl)2 radians per orbit for any elliptic orbit under a pure inverse-square force. where G is gravitational constant, M is mass of larger body, m is mass of smaller orbiting body, c is speed of light and l is angular momentum...
  29. L

    Stable Equilibrium of Two Hemispheres: a<3b/5

    Homework Statement A solid hemisphere with radius b has its flat surface glued to a horizontal table. Another solid hemisphere with radius a rests on top of the hemisphere of radius b so that the curved surfaces in contact. The surfaces of hemispheres are rough, meaning no slipping occurs...
  30. S

    Math and classical mechanics textbooks

    Hello everyone, my name is Silkia and I'm a new member. I am a pediatrician but as with Alejandro in another thread my real love has always been physics. In three occasions I had decided that this was my career choice but long "stories" short, I ended up in medical school. As an undergraduate I...
  31. L

    Solving for Acceleration of Mass on Cylinder w/ Frictionless String

    Homework Statement [/B] A solid cylinder of mass m and radius r lies flat on frictionless horizontal table, with a massless string running halfway around it, as shown in Fig. 8.50. A mass also of mass m is attached to one end of the string, and you pull on the other end with a force T. The...
  32. TehCylons

    Struggling with Newton's Second Law Equations

    Hello, I am a second year undergrad student majoring in Astronomy and Computer Science. I am having a hard time with my physics courses for the following reasons: 1) SmartPhysics is the text we use (if you can call it a text...). Basically it is an online HW and "pre-lecture" system that...
  33. J

    Goldstein Mechanics example motion of one particle in polar coordinates

    I have a course next semester on Classical Mechanics (mostly Lagrangian problems), for a second time. I'm ok for the theoretical preparation, but I'm trying to work ahead on problems and exercises, which was badly explained and without much of any resources. So, one of the sources to exercise on...
  34. A

    What level of mechanics should go for? | strategies for mastering problems?

    Hi everybody, The question sounds dumb, but I asked it, probably someone had the same experience, and can help me or give advice on it about what I'm going to do next ! I know calculus until the double integrals and I don't know enough about Lagrange multipliers ( Indeed, looking for intuitive...
  35. S

    Biomechanics Biceps Problem - Classical Mechanics (Moment Arms/Forces)

    Please let me know if I did this wrong or right, and if I did it wrong, please correct me :) 1. Homework Statement The biceps brachii, a muscle in the arm, connects the radius, a bone in the forearm, to the scapula in the shoulder (see below). The muscle attaches at two places on the scapula...
  36. BiGyElLoWhAt

    Hamiltonian in Classical mechanics?

    I've read a couple of places that a hamiltonian can be a tool used in classical mechanics and that it's eigenvalues are useful pieces of information. I've tried finding info on the subject matter, as I want to see something that actually requires linear algebra, or at least makes good use of it...
  37. T

    Classical Mechanics - Tranformations

    Homework Statement Consider a transformation to a relatively uniformly moving frame of reference, where each position vector ri is replaced by rli = ri − vt. (Here v is a constant, the relative velocity of the two frames.) How does a relative position vector rij transform? How do momenta and...
  38. R

    Classical Mechanics: Lightly Damped Oscillator Driven Near Resonance

    Hello Physics Forum! I have a question: The problem: For a lightly damped oscillator being driven near resonance in the steady state, show that the fraction of its energy that is lost per cycle can be approximated by a constant (something like 2pi, which is to be determined) divided by the Q...
  39. P

    Classical Mechanics Goldstein 2.16

    Homework Statement In certain situations, particularly one-dimensional systems, it is possible to incorporate frictional effects without introducing the dissipation function. As an example, find the equations of motion for the lagrangian ##L = e^{γt} (\frac{m\dot{q}^2}{2} - \frac{kq^2}{2})##...
  40. F

    Confusion about gradient in classical mechanics

    I'm currently going over some mechanics notes and am confused about the following situation: In the book I'm looking at, it describes two particles absent of external forces, only exerting a force on each other. In deriving a potential energy equation for the two, it goes on to say that if the...
  41. T

    Classical Mechanics - Moving Object in 3D space

    Homework Statement Hello, i have the following task, which should actually not be too hard, but for for some reason i cannot figure out the answer. Consider an Object with 1 kg mass in 3D space with coordinates \vec r = [x(t), y(t), z(t)]. Like Shown in the attachment, z:= e^{ax} and...
  42. C

    Difficulty following example in Taylor's Classical Mechanics

    http://i.imgur.com/GP6QorG.jpg I don't follow the integration in it. I'm assuming Fx(x,0) and Fy(1,y) are the partial derivatives of F with respect to x and y, respectively, but given that, I can't seem to get my head around the result where the partial with respect to x is Fx = (x, 0) instead...
  43. S

    Collisions in classical mechanics

    The only force really considered in classical mechanics is gravity. And yet, we often have problems involving collisions and friction, which are intrinsically electrical phenomena, and thus outside the scope of classical mechanics. We have laws such as conservation of momentum which is used for...
  44. C

    Book recommendation for classical mechanics

    Hello everyone, I have to choose a book for classical mechanics. After reading a lot through the forum, I find that the book by A.P French and the one by Kleppner is a good buy for my undergraduate course in classical mechanics. Also, is the book by Mary Boas for Mathematical methods a good...
  45. B

    Hamiltonian Noether's theorem in classical mechanics

    How does one think about, and apply, in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity \sum_{i=1}^n \frac{\partial \mathcal{L}}{\partial ( \frac{d y_i}{dx})} \frac{\partial y_i^*}{\partial \varepsilon} -...
  46. E

    Learning Electromagnetism before classical mechanics?

    Hi all, So basically I would like to know if it's possible. I'm a first year undergrad and I did classical mechanics first semester but I didn't do that well in it. So I'm not sure if I need to use my holidays to catch up with it before we do Electromagnetism during second semester. I would...
  47. tridianprime

    Good book for First Course in Calculus based Classical Mechanics

    I have taken a look at Kleppner and Kolenkow and that seems around the right level of difficulty but I was wondering if there were any other books that worked well alongside the Walter Lewin lectures on OCW. Would K&K? Also, where does K&K go up to? Does it include all undergraduate...
  48. J

    Derivation in classical mechanics

    I'm studying classical mechanics and I'm stumbling in the quantity of differential identities. Being S the action, H the hamiltonian, L the lagrangian, T the kinetic energy and V the potential energy, following the relationships: But, the big question is: that's all? Or has exist more...
  49. S

    Classical mechanics - small movements around equilibrium

    Homework Statement Two cylinders, that can rotate around their vertical axis, are connected with a spring as shown in the picture. Moment of inertia ##J## is the same for both and they also have the same radius ##R##. Distance between the axes is ##L##. Spring with constant ##k## is ##d## long...
  50. S

    Classical Mechanics or General Physics?

    I'm thinking about being a physics major with a double major in Earth Science. At my college Classical Mechanics is a required course for a physics major, whereas General Physics is required for the Earth Science major. There is an option at my school to take General Physics instead of Classical...
Back
Top