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.

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  1. CassiopeiaA

    A Symplectic Condition For Canonical Transformation

    I am reading Chapter 9 of Classical Mech by Goldstein.The symplectic condition for a transformation to be canonical is given as MJM' = J, where M' is transpose of M. I understood the derivation given in the book. But my question is : isn't this condition true for any matrix M? That is it doesn't...
  2. Elvis 123456789

    Courses Partial Differential Equations vs Classical Mechanics 2?

    Hello everyone. So I wanted to get some opinions on what some of you thought was a better choice, as far taking PDE's or classical mechanics 2 goes. First let me start off by giving a little info; I've already taken calc 1-3 and ordinary differential equations, physics 1 & 2...
  3. K

    Thoughts Experiment about Frame of References

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  4. N

    Classical Mechanics: Retarding force on a satellite

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  5. V

    I Why exactly does the ocean bulge on both sides of the Earth?

    Here's what my prof says: "Define F_{mean} to be the mean force, F_close to be the force on the side of the Earth closer to the moon, and F_far to be the force on the side of the Earth furthest away from the moon. On the closer side the net force is F_close - F_mean > 0 On the further side the...
  6. patrickmoloney

    Rotational Motion (Neutron Star)

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  7. AntonPannekoek

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  8. L = K - U

    Infinite Atwood Machine (Morin Problem 3.3)

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  9. P

    Solving Part c of Repulsive Force Homework Problem

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  10. Hercuflea

    Sailboat Speed Question: Can a Motor Increase Speed Beyond 10 Knots with Sails?

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  11. A

    Finding the force of constraint--compound pendulum on spring

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  12. B

    Height of the rise of the object attached to the spring ?

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  13. S

    Calculate the Orbital Radius of a Planet

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  14. B

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  15. Arij

    How Does Frequency Depend on Gravity in Classical Mechanics?

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  16. B

    Maximum uniform speed on a arc of a circular path ?

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  17. dexterdev

    A Can a molecular dynamics simulation enter a limit cycle?

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  18. P

    I Numerical Calculus of Variations

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  19. 1

    Center of mass of a sphere with cavity removed

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  20. 1

    How do I find the equation of motion for this object?

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  21. J

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  22. R

    Find x(t) with Kx Force and Mass m | KxForce

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  23. Faisal Moshiur

    Classical Mechanics Book Recommendation

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  24. weezy

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  25. A

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  26. D

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  27. Cocoleia

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  28. weezy

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  29. S

    Rocket Launch: Achieving Escape Velocity w/ Fuel-Mass Ratio of 300

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  30. INAM KHAN

    I Classical Mechanics v Quantum Mechanics

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  31. Cocoleia

    Block attached to a cord on an inclined plane

    Homework Statement I have a block of mass M attached to a cord of mass m on an inclined plane of angle θ . A force F is pulling the cord & block up the plane. I have to find the force exerted on the block by the cord. The surface is frictionless Homework Equations F = ma The Attempt at a...
  32. Cocoleia

    Block projected up inlcline with initial speed

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  33. Gopal Mailpalli

    Classical Good book for Lagrangian and Hamiltonian Mechanics

    This book should introduce me to Lagrangian and Hamiltonian Mechanics and slowly teach me how to do problems. I know about Goldstein's Classical Mechanics, but don't know how do I approach the book.
  34. certainice

    Energy principle example problem in classical mechanics book

    Homework Statement A man of mass 100 kg can pull on a rope with a maximum force equal to two fifths of his own weight. [Take g = 10 ms^2] In a competition, he must pull a block of mass 1600 kg across a smooth horizontal floor, the block being initially at rest. He is able to apply his maximum...
  35. P

    How Do Polar Coordinates Explain a Bead's Velocity on a Rotating Wheel?

    Note: All bold and underlined variables in this post are base vectors I was reading the book 'Introduction To Mechanics' by Kleppner and Kolenkow and came across an example I don't quite understand. The example is this: a bead is moving along the spoke of a wheel at constant speed u m/s. The...
  36. F

    Hamiltonian as the generator of time translations

    In literature I have read it is said that the Hamiltonian ##H## is the generator of time translations. Why is this the case? Where does this statement derive from? Does it follow from the observation that, for a given function ##F(q,p)##, $$\frac{dF}{dt}=\lbrace F,H\rbrace +\frac{\partial...
  37. VitorPAguiar

    What are the aspects that can help a car to flip in a turn?

    I am not sure if this is the right place to ask it, but this is a question that I thought today, and it gave me some curiosity to understand. Imagine that a car will curve, we can say the turn is a bit tight , what are the factors that can help it to flip? I was wondering about some aspects...
  38. steele1

    Prove area of triangle is given by cross products of the vertex vectors....

    Homework Statement The three vectors A, B, and C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by 1/2|(BxC)+(CxA)+(AxB)|. Homework EquationsThe Attempt at a Solution I know that the magnitude of the cross product of any two vectors...
  39. L

    Oscillations: mass in the center of an octahedron -- eigenvalues?

    You have an infinitesimally small mass in the center of octahedron. Mass is connected with 6 different springs (k_1, k_2, ... k_6) to corners of octahedron. Equilibrium position is in the center, you don't take into account gravity, only springs. Find normal modes and frequencies. Relevant...
  40. S

    A Planar orbit of planets around sun

    Imagine thee planets interacting through gravity, mathematically how should they come and rotate in a same plane, like planets and sun?
  41. R

    Hi, how to find the magnitude of a rotating vector?

    i get stuck in how to find the magnitude of rotating vector . why say that |dA/dt|=A(dθ/dt) but who we can derive it or interpret this fact
  42. UnterKo

    Can Gravity Make a Hoop Rise Off Its Support When Beads Slide Down?

    Hello, I've got a problem and I have no idea how to start. I'll be happy for any hint. Thanks Homework Statement Two beads each of mass m are at the top (Z) of a frictionless hoop of mass M and radius R which lies in the vertical plane. The hoop is supported by a frictionless vertical support...
  43. P

    Trajectory of pendulum in frame of rotating disk under it

    Homework Statement Consider the pendulum depicted in the adjacent figure: a mass m is attached to non stretching chord of length `. Directly below the pendulum is a circular disc rotating with constant angular velocity w. We attach to the disk a frame whose x-axis is in the plane of the...
  44. J

    Classical Spivak's Physics for Mathematicians: Mechanics

    Hello, I will be enrolling in an undergraduate Classical Mechanics course and I was wondering if the book by Spivak "Physics for Mathematicians: Mechanics" would help me understand the concepts more in depth than usual. Until the time that I will be taking the course, I will already have...
  45. H

    Orbit: impulse making orbit spherical

    Homework Statement A satellite moving in a highly elliptical orbit is given a retarded force concentrated at its perigee. This is modeled as an impulse I. By considering changes in energy and angular momentum, find the changes in a (semi major axis) and l (semi latus rectum). Show that \delta...
  46. D

    Asteroid deflected by Earth -- effect on Earth

    Homework Statement Suppose the asteroid of [other problem] has a mass of 6 \times 10^{20} \textrm{kg} . Find the proportional change in the kinetic energy of the Earth in this encounter. What is the change in the semi-major axis of the Earth's orbit? By how much is its orbital period...
  47. F

    Classical Need a Classical Mechanics book that covers these topics

    I'm a freshman in Computer Engineering at a university. I have a Classical Mechanics course that will cover these topics: Newton's law of motion Vector Algebra Equilibrium of bodies Plane Trusses First moment of area, centroid, etc. Calculation of virtual displacement and virtual work...
  48. D

    Scattering of two charged particles

    Homework Statement Two identical charged particles, each of mass m and charge e, are intitialy far apart. One of the particles is at rest at the origin, and the other approaching it with velocity v along the line x=b, y=0 where b=e^2/2 \pi \epsilon_0 mv^2. Find the scattering angle in the CM...
  49. D

    Density of star from hydrostatic equilibrium and pressure

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  50. Q

    A Is this constraint nonholonomic or not?

    I really want to know whether this equation is nonholonomic or not. (As far as I know, Nonholonomic constraint has a term of velocity and do non-integrable. But this formula does not dependent on a path, because it is a total differential form.)
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