# What is Classical dynamics: Definition and 48 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. ### I Frame Transformation in rigid bodies

I'm using rigid body dynamics/kinematics in robotics stuff but I don't have a background in mechanics, I'm interested in understanding the kinematics of frame transformations for rigid bodies. Suppose we have two reference frames fixed on a rigid body, F_1 and F_2 and a transformation T which...
2. ### Angular Acceleration when accounting n-reference frames

Hello, I understand the equation that describes the angular accelerator when 3 reference frames are involved is: Now I would like to ask what is the resulting equation when accounting more than 3 reference frames, i.e. when n-reference frames are involved. Thank you.
3. ### Frequency of oscillations given 3 springs at angles ##\frac{2\pi}{3}##

I am attaching the solution given, but I am not convinced with the approach. I am also asking for some suggestions and hints if I am wrong or is there any other way around. The thing I do not understand is the arguments from geometry they have made. How they can conclude the extension of spring...
4. ### Why Does a Particle Not Remain at x(t)=0 in a Negative Quartic Potential?

This question is from Collection of Problems in Classical Mechanics by Kotkin & Serbo, here, the answer is given as the following: However, the graph of ##-Ax^4## looks like: so shouldn't the trajectory be just ##x(t)=0##?
5. ### Understanding Kinetic Energy: Moment of Inertia and Rotational Motion

Consider the above setup. Here, to get the kinetic energy of the body, the moment of inertia with respect to the ##y-##axis has to be calculated. This can be done in two ways: 1. The moment of inertia of the rotation around the center of mass is ##\Theta_s##, then the kinetic energy is...
6. ### I Requirement of Holonomic Constraints for Deriving Lagrange Equations

While deriving the Lagrange equations from d'Alembert's principle, we get from $$\displaystyle\sum_i(m\ddot x_i-F_i)\delta x_i=0\tag{1}$$ to $$\displaystyle\sum_k (\frac {\partial\mathcal L}{\partial\ q_k}-(\frac d {dt}\frac {\partial\mathcal L}{\partial\dot q_k}))\delta q_k=0\tag{2}$$ However...
7. ### Classical Classical Dynamics Book for Self-Study.

Hello. Can someone guide me in choosing the right book? My choice was Marion's book, but I did not understand some topics well ...
8. ### I Proving that the Lagrangian of a free particle is independent of q

One of the first things Landau does in his Mechanics book is give an argument as to why the Lagrangian of a free particle must be our conventional kinetic energy. Heuristically, he justifies it, but leaves out the details, perhaps being too obvious. They aren't obvious to me. While in free space...
9. ### I Star with quadrupole in a binary system violates Newton's 3rd Law?

Assume that, in a binary system, one (and only one) of the two stars has a non-zero quadrupole moment. Then the other star feels the usual gravity force $F_g$ plus an additional force $F_q$ coming from the quadrupole potential. On the other hand, the first star feels only the usual gravity force...
10. ### Maximum bending moment and maximum deflection of the spring?

How can I find the maximum bending moment and maximum deflection for a spring? It would be very helpful if you could explain the specific procedure and formula in an easy-to-understand manner. that's all, thank you very much.
11. ### A Change of a vector in a rotating coordinate system

Goldstein 3 ed, pg 171, under" rate of change of a vector " : The author derives the relationship between the change of a vector in a stationary and rotating coordinate system. In the process he uses this assumption :>It is no loss of generality to take the space and body axes as...
12. ### A Rotation matrix and rotation of coordinate system

If we change the orientation of a coordinate system as shown above, (the standard eluer angles , ##x_1y_1z_1## the initial configuration and ##x_by _b z_b## the final one), then the formula for the coordinates of a vector in the new system is given by ##x'=Ax## where...
13. ### A Doubt in a step while deriving Bertrand theorem

Goldstein 2nd ed. In its Appendix is given the derivation of Bertrands Theorem.Here ##x=u-u_0## is the deviation from circularity and ##J(u)=-\frac{m}{l^{2}} \frac{d}{d u} V\left(\frac{1}{u}\right)=-\frac{m}{l^{2} u^{2}} f\left(\frac{1}{u}\right)## If the R.H.S of A-10 was zero, the solution...
14. ### A Dissipation function is homogeneous in ##\dot{q}## second degree proof

We have Rayleigh's dissipation function, defined as ## \mathcal{F}=\frac{1}{2} \sum_{i}\left(k_{x} v_{i x}^{2}+k_{y} v_{i j}^{2}+k_{z} v_{i z}^{2}\right) ## Also we have transformation equations to generalized coordinates as ##\begin{aligned} \mathbf{r}_{1} &=\mathbf{r}_{1}\left(q_{1}, q_{2}...
15. ### I How do shockwaves in a 1D linear lattice work?

I am struggling to understand shocks in a one dimensional lattice with a linear spring connecting the masses. Say I have a one dimensional lattice with a linear spring constant, k and lattice spacing a. If the particles in the lattice has mass, m then my speed of sound c is a*sqrt(k/m). That is...
16. ### Failing in "Classical Dynamics": Seeking Advice for Pursuing a PhD

Hello, PF members. This is my first post here. I got my undergrad result for final semester few days ago and to my surprise it showed that I have failed in 'classical dynamics'. This is not at all possible as I clearly remember it being easy and quite simple. What bothers me more is that I had...
17. ### Solving 8.62: Frictionless Stick in Morin's Classical Mechanics

Homework Statement This is the problem 8.62(in screenshot) from Morin's textbook of Classical mechanics. I solved it using conservation of momentum in y direction. However in solution manual,he neglects the momentum in y direction by calling stick frictionless. What is this frictionless stick...
18. ### Can Lagrangian Method be Applied to Solve Rocket Motion Equations?

Homework Statement While solving equation of rocket motion with Newton's law in 1-d,I pondered to apply Lagrangian method on this. However, I didn't get correct result. Because I can eliminate last 2nd equation using last equation and get some other equation which is certainly not rockets...
19. ### Trouble solving an ODE and plotting its phase portrait

Mentor note: Moved from non-homework forum to here hence no template. So I was able to solve part 1.A of the first problem by hand, the phase portrait is a sideways parabola. However, I want to also show on this on mathematica. I want to solve the equation first and then plot the phase...
20. ### Given force as a function of x, how do I find the total energy?

Homework Statement F=-kx+kx3/α2 where k and α are constants and k > 0. Determine U(x) and discuss the motion. What happens when E=kα2/4? Homework Equations F=ma=mv2d/dx U=-∫Fdx The Attempt at a Solution The first part is easy. U(x) = kx2/2-kx4/4α2 Now I'm looking for what happens when E=kα2/4...
21. ### Possible error in Marion and Thornton's Classical Dynamics?

Homework Statement so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3, I've uploaded the page here The rotation matrix associated with 1.2a and 1.2b is \begin{pmatrix} \cos\theta &...
22. ### Set up the Lagrangian for a CO2 molecule

Homework Statement The carbon dioxide molecule can be considered a linear molecule with a central carbon atom, bound to two oxygen atoms with a pair of identical springs in opposing directions. Study the longitudinal motion of the molecule. If three coordinates are used, one of the normal...
23. ### Motion analysis of an accelerating wedge and a block

I don't understand the motion of an accelerating wedge and a block. I'd really appreciate if you make me understand the motion in both an inertial and a non inertial reference frame. Here's a figure I have made, a0 is the acceleration on the wedge with respect to an inertial frame, towards right.
24. ### Electron in orbit of around a single proton

Today I was doing some reading and I came across this topic. If we have a stationary hydrogen atom with a single electron in orbit around the nucleus and want to calculate the kinetic energy of the electron we would take the following approach. 1) Using Newton's second law: F = ma ⇒ FE = mac...
25. ### 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.
26. ### Problem in Classical Mechanics

Homework Statement I am stuck over a classical mechanics problem. I tried to solve it, but after having solved the first point, I got stuck on the second one. Here is the problem: >A mechanical structure is composed by 4 rigid thin bars of length $\ell = 8\ m$, mass $m = 5\ kg$ each one. Those...
27. ### I Is the Hamiltonian always the total energy?

I'm working on some classical mechanics and just got a question stated: Is the Hamiltonian for this system conserved? Is it the total energy? In my problem it was indeed the total energy and it was conserved but it got me thinking, isn't the Hamiltonian always the total energy of a system...
28. ### Motivation for Lagrangian mechanics

I know how to implement Lagrangian mechanics at a mathematical level and also know that it follows the approach of calculus of variations (i.e. optimisation of functionals, finding their stationary values etc.), however, I'm unsure whether I've grasped the physical intuition behind the...
29. ### 2-DOF problem with unknown stiffness and velocity

Homework Statement I have a 2-DOF system, whereby I have one body that is grounded by a spring (body A), and a second body (body B) attached to the first by a spring and a viscous damper. For body A, I know the velocity and amplitude (before body B is added). I think I also have the stiffness...
30. ### General Form of Canonical Transformations

Homework Statement How do I go about finding the most general form of the canonical transformation of the form Q = f(q) + g(p) P = c[f(q) + h(p)] where f,g and h are differential functions and c is a constant not equal to zero. Where (Q,P) and (q,p) represent the generalised cordinates and...
31. ### Classical Recommendation for rigorous intro books to mechanics and E&M

Hey guys I'm a sophomore in college currently taking physics 2(intro E&M), Multivariable calculus, and Differential Equations. I was hoping some of you guys could recommend some good books for intro mechanics and E&M. I'm currently using University Physics by Young in my E&M class, and I used...
32. ### Classical Dynamics -- Falling chain and energy conservation

Homework Statement The statement of the question is:A chain of uniform linear mass density ##\rho##, length ##b## and mass ##M## hands as shown in the figure below. At time t=0, the ends A and B are adjacent, but end B is released. Find the tension in the chain at point A after end B has...
33. ### Problem 2 rigid rods - Greenwood - Classical Dynamics

From "Greenwood Donald T. - Classical Dynamics", Chapter 1, Section 1-4 (virtual work), Example 1-4: https://books.google.it/books?id=x7rj83I98yMC&lpg=PP1&hl=it&pg=PA26#v=onepage&q&f=false 1) There are 3 mass points of the same mass m moving on a plane (even if the text doesn't specify this)...
34. ### Classical Dynamics Any help would be greatly appreciated

Homework Statement A mass m1 is attached to a fixed spring on a horizontal surface and attached across a pulley (ignore the pulley mass) to another freely hanging m2. Write the Lagrangian in terms of a single parameter. Find the equation of motion and determine the frequency of oscillation...
35. ### Classical Dynamics of Particles & Systems

This is an image of Classical Dynamics of Particles & Systems, chapter 1 In deriving the equations for the rotation of a coordinate system I understand the equations 1.2a & 1.2b b, but why is the projection of x2 on the x'1 equal to ab +bc and why is the vector de equal to the vector Of? I...
36. ### Classical Classical Dynamics: A Contemporary Approach by José and Saletan

Author: Jorge José and Eugene Saletan Title: Classical Dynamics: A Contemporary Approach Amazon Link: https://www.amazon.com/dp/0521636361/?tag=pfamazon01-20
37. ### Classical Classical Dynamics of Particles and Systems, by Jerry Marion and Stephen Thornton

Author: Stephen T. Thornton (Author), Jerry B. Marion (Author) Title: Classical Dynamics of Particles and Systems Amazon Link: https://www.amazon.com/dp/0534408966/?tag=pfamazon01-20 Prerequisities: Calculus, Ordinary and Partial Differential Equations, Introductory Physics Level...
38. ### How is Greenwood's Classical Dynamics?

My friend recommend this book to me. Actually, I don't have enough time to read Goldstein. But this is book is not so thicker as Goldstein's. May I use this book as a substitution?
39. ### Classical Dynamics 2/II/15B 2008

Hi, I'm doing this Classical Dynamics section II question which can be found here (http://www.maths.cam.ac.uk/undergrad/pastpapers/2008/Part_2/list_II.pdf ) on page 27. I have done most of the question but am unsure about the last part. Specifically using Hamilton's equations to show there's...
40. ### Is this system symetric enough? - classical dynamics

I'm designing a satellite( flying in formation). It looks like 3 couples of daughter-satellites(180degree apart) orbiting around the mother satellite in 3 orthogonal planes to measure flyby anomally effect. I want to measure the effect in 3-separate directions. But I'm afraid that the orbiting...
41. ### Classical Dynamics: Given v(x), find F(x), x(t), and F(t).

Homework Statement The speed of a particle of mass m varies with the distance x as v(x) = (alpha)*x-n. Assume v(x=0) = 0 at t = 0. (a) Find the force F(x) responsible. (b) Determine x(t) and (c) F(t)Homework Equations Likely: F = maThe Attempt at a Solution I obtain a(x) = -n(alpha)x-(n+1) So...
42. ### Analytical Classical Dynamics: An intermediate level course

Moderation note: In reference to http://farside.ph.utexas.edu/teaching/336k/lectures.pdf Lagrangian(L) and Hamiltonian(H), Dear Greg I am studying the L and H. If kinetic energy(K) and potential(U) are given it seems that L=K-U. Hamilton defines (p_i, dot q_i being components of momentum...
43. ### Book is Classical Dynamics of Particles and Systems

book is "Classical Dynamics of Particles and Systems" hello again all. im just preparing for my first semester at a real university. I transferred from community college. i will be taking mechanics and the book is "Classical Dynamics of Particles and Systems" by Thornton. I was wondering if...
44. ### Marion and thornton classical dynamics

Hello, Does anyone have marion and thornton's classical dynamics book? I have a possible error that I wanted to point out. Actually, goldstein's classical mechanics book would work also since I found the same "error" in there as well.
45. ### Analytical Classical Dynamics: An intermediate level course

A complete set of lecture notes for an upper-division classical dynamics course. The course concentrates on those aspects of classical dynamics which can be studied analytically. Topics covered include oscillations, Keplerian orbits, two-body scattering, rotating frames of reference, rotation of...
46. ### Classical dynamics recent progress

Hi all I am wondering about recent developments of classical dynamics. It seems most physicists are now devoted to quantum world. Is there any effort to broaden the scopes of classical world? Thanks
47. ### Analytical Classical Dynamics: Newton's Laws

[SOLVED] Analytical Classical Dynamics: Newton's Laws Homework Statement Consider a system of N mutually interacting point objects. Let the ith object have mass mi and position vector ri. Suppose that the jth object exerts a central force fij on the ith. In addition, let the ith object be...
48. ### Classical Dynamics prob, please.

The question is as follows: The height of a hill (meters) is given by [z=(2xy)-(3x^2)-(4y^2)-(18x)+(28y)+12], where x is the distance east, y is the distance north of the origin. a). where is the top of the hil (x,y,z) and how high is it (z=?)? b). How steep is the hill at x=y=1, that is...