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. 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...
  2. 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...
  3. 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...
  4. 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...
  5. 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...
  6. 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...
  7. 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...
  8. D

    Configuration Space In Classical Mechanics: Definition

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  9. 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...
  10. F

    Classical Mechanics, Coupled Harmonic motion

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  11. E

    Continuum mechanics vs Classical mechanics are they the same?

    Will taking a course is continuum mechanics give me the same background as in classical mechanics or would I need to take both separately? Can anyone explain the difference if there is one between classical mechanic vs continuum mechanics in simple nontechnical terms.
  12. J

    What Is the Best Classical Mechanics Book for Deep Conceptual Understanding?

    Im pretty good at Mechanics but I need a "feel good" book which can complement and help me strengthen my concepts of mechanics very well. I like thorough explanations so I can be conceptually good and in a position to attempt most questions. Also needs to have good worked examples. Please let me...
  13. C

    Which is the best book in modern theoretical classical mechanics?

    Hi! I am a very mathematically-oriented physicist. Since I never plan in making contact with "dirty" mechanics like robotics, structural problems or force diagrams, I want a book that prepares me for the mathematical/theoretical foundations of mechanics so that I can transition more smoothly to...
  14. M

    On the principle of least action in classical mechanics

    The principle of least action applicable in an uniform field can be obtained as follows: Particle A \vec{a}_A = \vec{a}_A \int \vec{a}_A \cdot d\vec{r}_A = \int \vec{a}_A \cdot d\vec{r}_A \int \vec{a}_A \cdot d\vec{r}_A = \Delta \; {\textstyle \frac{1}{2}}\vec{v}_A^2 \int \vec{a}_A...
  15. P

    Some questions regarding classical mechanics in space

    I'm working on a project for a space habitat, and I want to have the math to back it up. Sorry if some of these seem obvious or too simple, but I'm here to learn. By the way this is not homework, it's just something I do in my spare time. And if you have the links where I can learn more about...
  16. T

    Terminal Velocity In Glycerin 2.10 in Classical Mechanics

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  17. M

    Classical Mechanics - Coriolis Force

    Homework Statement This is a fairly general problem that came up while trying to model a system. Given a rotating disk and an inertially fixed object, how is the fictional coriolis force handled? For example, if there is a dot on the ground below a sheet of transparent plastic rotating at...
  18. R

    Classical mechanics - finding distance D in terms of velocity

    Homework Statement "A passenger (mass m) initially at rest steps out of an airplane. Assume down is the positive x-axis and put the origin at the airplane. Assume the air resistance force is linear in the velocity so F(air)= -mbv. Find the distance D he has fallen when his velocity is...
  19. V

    How Is Angular Velocity Calculated in This Classical Mechanics Scenario?

    Homework Statement A particle has a velocity u = -V0 i + V0 j and position (d,0) at t=0. At any time t its position in polar coordinates is (r,theta) and velocity V = V0 cos theta i + (V0-V0sin theta) j. At t =t, angular velocity of the particle at the origin will be -----------------...
  20. R

    Need to find online classical mechanics course

    Hi, I'm currently a physics major attempting to earn my bachelor's degree. I was just told by the tiny physics department at my school that they won't be offering the classical mechanics course that I need in order to graduate before that fateful date, they suggested that I add an additional...
  21. R

    Confusion regarding fundamental classical mechanics question

    A block is resting on a frictionless surface as shown in the figure attached with this post. Calculate the minimum force F required so that the block will topple? The dimensions of the block, free body diagram and other details are there in the picture attached. Now, since the surface is...
  22. S

    Classical mechanics equation of motion

    Homework Statement A point mass m moving along the z axis experiences a time dependent force and a fricitional force. Solve the equation of motion m\ddot{z} = -m\gamma\dot{z} + F(t) to find v(t) = \dot{z}(t) for the initial velocity \dot{z}(0) = v_0 Hint: what is the time derivative of...
  23. S

    Classical mechanics with time dependent force

    Homework Statement A point mass m is exposed to a time dependent force F(t). Determine the position r(t) of the point mass for the initial conditions r(0) = r_{0}and v(0) = v_{0} Homework Equations The Attempt at a Solution \sumF= ma F_{z}(t) - mg = ma a = 1/m F_{z}(t) - g...
  24. N

    Best way to study classical mechanics?

    I am taking calculus based physics I (classical mechanics) in a few days. I'm shooting for 100s on my tests so I need to be diligent. What is the best way to study classical mechanics? What I plan to do is take notes on the chapter before lecture, and after I will do all the problems (not...
  25. M

    Why Do First-Year Grad Students Take Classical Mechanics?

    Why do first-year grad students take classical mechanics, besides those wanting to analyze mechanical systems? This would be a course along the lines of Goldstein, etc. Do some of the concepts/methods show up later in quantum mechanics, nuclear physics? If they skipped this mechanics...
  26. A

    Good books on classical mechanics

    Can anyone give me some suggestions?Thanks.
  27. L

    Are there 'complex' numbers in classical mechanics?

    Wondering if it is only the formulae of quantum mechanics that routinely include complex numbers (a real component plus an imaginary one, e.g. i (the square root of -1)). If so, doesn't this immediately suggest (or even demand) that the (un)reality of the quantum realm is fundamentally unlike...
  28. L

    Classical mechanics with a mass on a light elastic string

    Classical Mechanics Homework question Question - A light elastic string AB of natural length L and spring constant K, lies slack on a horisontal plane. A particle of mass m also at rest, is attached to end A of the string. The other end B is pulled along the plane with constant velocity V...
  29. E

    Classical Mechanics and Lagrangian/Hamiltonian Formalism: A Quick Review

    I'm beginning a directed study in QFT this fall and my supervising instructor told me I'd need to know some basics of Lagrangian and Hamiltonian Mechanics before we began (he also told me I needed to go back and review Perturbation Theory) since I'd need to know the formalism I guess? I've...
  30. fluidistic

    Rigid body kinetic energy+ constraints (upper level classical mechanics)

    Homework Statement Using the corresponding constraints conditions, calculate the kinetic energy of 1)A homogeneous cylinder of radius a that rolls inside a cylindrical surface of radius R>a.Homework Equations My toughts: I hope they meants "roll without slipping". Let's consider this case...
  31. fluidistic

    Classical mechanics, principal moments of inertia of a rigid body

    Homework Statement Determine the principal moments of inertia of a circular cylinder with radius R and height h. Homework Equations Not sure. The Attempt at a Solution This is the first problem of this kind I attempt to solve. From what I've read on wikipedia, the tensor of...
  32. fluidistic

    Classical mechanics: Central potential, trajectory

    Homework Statement Determine the possible trajectories of a particle into the following central potential: U(r)=U_0 for r< r_0 and U(r)=0 for r>r_0.Homework Equations Not sure. What I used: Lagrangian+Euler/Lagrange equations.The Attempt at a Solution I used polar coordinates but I'm not sure...
  33. A

    Classical Mechanics for an Engineer?

    I'm an aerospace engineering major. I'm wondering if, in the future (perhaps after graduation), a treatment of classical mechanics under Taylor's book would be useful to me. I will be taking classes on statics and dynamics, but after that, there doesn't seem to be any further treatment of...
  34. fluidistic

    Classical Mechanics, constraint motion problem

    Homework Statement A particle of mass m moves under a uniform gravitational field along a rod which moves in a vertical plane with a constant angular velocity \vec \Omega. Write down the motion equations of the particle and calculate the constraint force. Is the energy conserved...
  35. fluidistic

    Classical Mechanics, cycloid pendulum

    Homework Statement The cycloid pendulum consists of a particle under the effect of a constant gravitational field (\vec g = -g \hat y) that moves without friction over a curve described parametrically by x=a(\theta + \sin \theta) and y=a(1-\cos \theta ). 1)Write down the Lagrangian and the...
  36. Y

    Exploring Classical Mechanics: Introductory Texts and Recommended Resources

    What is the typical material covered in such classes? Is there a common textbook used by most colleges that I could look through? Can someone suggest a good book from Dover publications that I can pickup cheaply to serve the same purpose? Much appreciated.
  37. O

    Classical mechanics energy and momentum

    Homework Statement I try to solve the problem 3.5 in Kleppner Kolenkow ”An introduction to Mechanics” using various approaches but end up with wrong answers. The problem is: 3.5 A circus acrobat of mass M leaps straight up with initial velocity v0 from a trampoline. As he rises up he takes...
  38. fluidistic

    Angular momentum of a particle in Classical Mechanics

    Homework Statement Calculate the Cartesian expressions and the value of the modulus of the angular momentum in cylindrical coordinates of a particle whose coordinates are (r, \phi, z).Homework Equations L=T-V, \vec P = \sum _i ^3 \frac{\partial L}{\partial \vec {\dot q_i}}, \vec M = \sum _i^3...
  39. P

    Retaking Classical Mechanics for Higher GPA

    I am a Physics major, just completed my junior year. During my fall semester I took the first level to the upper level Classical Mechanics sequence and received a C. I know that this was because I was working part time at that time so I was not able to put in as much time as I should have into...
  40. S

    Classical Mechanics and E&M introductory books

    Hi, I looking for books that have practice problems (with explanations would be nice) on general introductory level Calc. based Classical Mechanics. And for Electromagnetism I'm looking for an introductory book that has practice problems. I haven't taken Multivariable Calc. yet (I'll be...
  41. G

    Transition: Classical Mechanics to Quantum Mechanics

    Imagine that I have a system that is described classically by a given Hamiltonian which is a function of a given set of parameters q and their canonical conjugate momenta p=\frac{\partial L}{\partial \dot{q}}. Then, I will say that the quantum description of the same system is guided by setting...
  42. M

    Regarding College Classical Mechanics and the mathematics therein

    I'll be attending college in a few months, and I would like to know what mathematics to study in order to understand my classical mechanics class. Could anyone help me? I've heard that I should know ODEs and PDEs but I didn't think such math was required. Is this true? And what should I be...
  43. J

    Classical Mechanics Textbook: Beyond Algebra Required?

    Okay, I have this textbook about Classical Mechanics. It is NOT a high school textbook, it's like a college textbook, which requires beyond algebra. I also have calculus textbook, but I have not mastered multivariable calculus yet. If I do master this, will it help me finish Classical Mechanics...
  44. D

    Mathematical prerequisites for Classical Mechanics

    So, I am about to read Landau's and Lifschitz's textbook on Classical Mechanics. What kind of mathematics I should be already familiar with in order to completely understand the above mentioned material? Would real-variable calculus and linear algebra be sufficient for the task? Thanks for all...
  45. 2

    Complex formulation of classical mechanics

    Looking at a path of system state (x(t),v(t)) as a vector, the Lagrangian strangely is a scalar function of pairs of coordinates of the vector. If, on the other hand, the complete state of a system was captured in a single complex number x+iv, a complex analogue of the Lagrangian would simply...
  46. A

    What is the difference between Mechanics and Classical Mechanics?

    Sorry if this sounds like a dumb question, but at Georgia Tech, many engineering majors take a class in mechanics (required) and classical mechanics (not required, but it's an option). I just finished mechanics in my high school AP Physics class (which should be similar in content to a college...
  47. T

    Critically damped oscillator: Classical mechanics help

    Homework Statement A critically damped oscillator with natural frequency \omega starts out at position x_0>0. What is the maximum initial speed (directed towards the origin) it can have and not cross the origin? Homework Equations For the case of critical damping...
  48. B

    Cable on a Table (classical mechanics)

    Homework Statement A perfectly flexible cable has length l. Initially, the cable is at rest, with a length of it hanging vertically over the edge of a table. Neglecting friction, consider the cable's motion as it slips off the edge of the table. (a) Show that the length hanging over the edge...
  49. N

    [Classical Mechanics] Just need some conceptual help (rolling and friction)

    Homework Statement "A ball with radius R and mass m turns around a horizontal axis through his center with an angular speed \omega_0. In that condition the ball, without an initial velocity in the center, is put on top of a table. The friction coëfficient between the ball and the table is µ...
  50. snoopies622

    How Does Reference Frame Affect Kinetic Energy Calculations?

    I just thought of this. I think I know the answer to it now, but it took me a little bit of thinking. Maybe someone who teaches high school physics might find it useful. - - - - - I have a battery-powered toy car. I turn it on and it accelerates from speed 0 to speed 1. (I'm leaving...
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