Classical mechanics Definition and 1000 Threads

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...

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...

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...

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...

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

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

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...

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...

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...

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...

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...

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...

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...

Homework Statement Assume that the pressure p in a star with spherical symmetry is related to the density \rho by the (distinctly unrealistic) equation of state p= \tfrac12 k\rho^2, where k is a constant. Use the fluid equilibrium equation obtained in Problem 23 to find a relation between \rho...

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.)

Recently I lend the Classical mechanics book written by Goldstein from the library, In the last page, someone scribbled this problem without any solution, I am just curious and want to give a try the problem mentioned below. I just want to know whether my approach and my solution is correct or...

Homework Statement The orbit of an electron (-e) around a nucleus (Ze) is a circular orbit of radius a in a plane perpendicular to a uniform magnetic field \textbf{B}. By writing the equation of motion in a frame rotating with the electron, show that the angular velocity \omega is given by one...

Homework Statement Show that Kepler's third law, \tau = a^{3/2}, implies that the force on a planet is proportional to its mass. Homework Equations 3. The Attempt at a Solution [/B] I haven't really attempted anything. I'm not sure what the question is going for. What can we assume and use?

Homework Statement The potential energy of a particle of mass m is V(r) = k/r + c/3r^3 where k<0 and c is a small constant. Find the angular velocity \omega in a circular orbit of radius a and the angular frequency \omega' of small radial oscillations about this circular orbit. Hence show...

Homework Statement This question involves parts of other questions, so I will state the relevant parts and essentially what the question is asking. It is from Kibble Classical Mechanics, Chapter 4, Question 22. If more information is needed I will provide. We have a satellite that orbits the...

Hello, I have used Greiner's "Quantum Mechanics: An introduction" and found it to be awesome, bridging the ga between undergraduate and graduate courses. So, I am thinking of buying some of Greiner's book to use for my other courses and I wanted to ask you what your opinions about the books in...

In the market, it has many many physics books teaching classical mechanics. Do you read one book only or a number of books? How do you make a choice?

I am a second year physics and I want to study CM in more depth than that of the general textbooks

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...

Homework Statement Show that the set of restricted canonical transformation forms a group. Verify this statement once using the invariance of Hamilton's principle under canonical transformation, and again using the symplectic condition. Homework Equations (Invariance of Hamilton's principle...

Homework Statement Say I have some planet in a circular orbit around a star, and I give it a small radial push (directly toward or directly away from the star). How would I describe the new orbit? I.e. how would I determine the equations of motion? h Homework Equations Kepler orbital radius...

Homework Statement Q1. What's the reason behind two identical objects interchanging their velocities upon head-on collision? Why can't just each individual particles just reverse its direction and keep traveling at its original speed? Kinetic energies and momentum would still be conserved. Q2...

How do I find torsion constant (Kt) of a spring which is bent, as shown in the image below

Hi there! First Post :D In a recent CM module we've been looking at coupled oscillators and the role of time translational invariance in the description of such physical systems. I will present the statement that I am having trouble understanding and then continue to elaborate. In stating that...

Homework Statement http://i.imgur.com/BV5gR8q.png Homework Equations d/dx ∂F/∂y'=∂F/∂y The Attempt at a Solution I have no problem with the first bit, but the second bit is where I get stuck. Since the question says the speed is proportional to distance, I have taken v(x)=cx where c is some...

Homework Statement Please see attached image :) Homework Equations Euler-Lagrange Equation \frac{\partial{L}}{\partial{q}} - \frac{d}{dt}\frac{\partial{L}}{\partial{\dot{q}}} = 0 L = T - V The Attempt at a Solution a. The potential energy V is the potential energy from the spring and the...

A block with mass m =7.1 kg is hung from a vertical spring. When the mass hangs in equilibrium, the spring stretches x = 0.23 m. While at this equilibrium position, the mass is then given an initial push downward at v = 4.5 m/s. The block oscillates on the spring without friction. 1)What is the...

My professor is mentoring me through learning GR over the next year with the goal of doing research with me in the long term in the field. I need to pick up a few things along the way. The summer is going to be spent mostly picking up the necessary material for jumping into Carroll's book, and...

I am asked to find the shape of a wire that will maximize the speed a sliding bead when it reaches the end point(Similar to the brachistochrone problem expect that the speed is to be maximized and not time minimized). But shouldn't the speed at the end be independent of the shape of the wire...

Homework Statement I am supposed to calculate Lyapunov exponent of a damped, driven harmonic oscillator given by ## \ddot{x} + 2\beta \dot{x} + \omega_0^2 x = fcos(\omega t)## Lyapunov exponent is ## \lambda ## in the equation ## \delta x(t) = \delta x_0 e^{\lambda t} ## The attempt at a...

Homework Statement This was supposed to be an easy question. I have a question here that wants you to describe a yoyo's acceleration (in one dimension) using Lagrangian mechanics. I did and got the right answer. Now I want to use Hamilton's equations of motion but I get a wrong number. Here is...

Hi guys i have a problem and I'm not able to solve it. I have a cube lying on the ground that is hinged on a side in contact with the floor. Right above the hinge there is a rod hinged (at the start time the rod is horizzontal) and it is long enough to touch the cube when it fall...how much the...

They are subjective even in the classical, nonrelativistic mechanics of a pendulum, since the notions appear when you try to relate the theory to a real pendulum. In classical, nonrelativistic mechanics, the interpretation of the words ''observation'', ''experiment'' and ''measurement'' needed...

Hi I am a high school student and I am about to graduate. within few months I am planning to study physics field if I pass the University selection. I love physics after I found the beauty of Quantum Mechanics, General Relativity, Thermodynamics, etc. Although I want to dive in those field, I...

What are Hamiltonian/Lagrangian Mechanics and how are they different from Newtonian? What are the benefits to studying them and at what year do they generally teach you this at a university? What are the maths required for learning them?

I have been asked by someone if it is true that in general, for a constantly accelerating reference frame, i.e. a non-inertial reference frame, the acceleration of a particle (as observed in this frame) due to the corresponding fictitious force is independent of its mass. My response was yes...

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 conjugate momentum in...

Homework Statement Classical Mechanics: John Taylor[/B] (1.27) The hallmark of an inertial reference frame is that any object which is subject to a zero net force will travel in a straight line at a constant speed. To illustrate this, consider the following experiment: I am standing on the...

im 16,love physics, who is about to graduate school, before that i decided that school was too slow for me, so i decided to skip right to the good stuff... did precalculus and 'How to Prove it' to start me on calculus. i just finished Apostol's calculus vol 1 to prepare me for handling the...

Hi, I'm new to the forum, I'd like some recommendations of books on classical mechanics. Too vague, right? I'm a CS student, with a great disposition for mathematics and great love for physics. I've learned one-variable calculus through Stewart and I'm starting linear algebra with Strang and...

Homework Statement This is Exercise 1.19 in Goldstein's Classical Mechanics 2nd edition. Self-study, not for a class. Two mass points of mass ##m_1## and ##m_2## are connected by a string passing through a hole in a smooth table so that ##m_1## rests on the table and ##m_2## hangs suspended...

Homework Statement I was recently assigned an assignment where my instructor told us to come up with an idea for a numeric classical mechanics problem that is solved by computer methods. Some ideas the instructor gave was to simulate motion of a sun-earth-moon system or simulate the tides of a...

1. Homework Statement FInd acceleration and tension. Take g=10m/s^2 2. The attempt at a solution By drawing the free body diagrams of every block and simultaneously solving all the equations, I got the answer acceleration= 30/7 m/s^2, which is also correct. But when I try to treat all the...

Homework Statement A force field in 2-d F~ = −kr(rˆ) with U(r) = k(r^2)/2 acts on a particle of mass m. The particle is now in a non-circular orbit. In terms of the particle’s angular momentum L and energy E, d) What is its closest approach to the origin? e) What is its furthest distance from...

I'm reading Goldstein's "Classical Mechanics", first chapter, and am confused about what's going on in equations of forces and work in systems of particles. For example, Goldstein calculates work done by all the forces, external and internal, in evolving the system from state ##1## to state...