Goldstein Definition and 56 Threads

I am using Nivaldo Lemos' "Analytical Mechanics" textbook and on section 2.4 (Hamilton's Principle in the Non-Holonomic Case) he uses Hamilton's Principle and Lagrange Multipliers to arrive at the Lagrange Equations for the non-holonomic case. I don't understand why it is assumed that the...

So I am thinking of going through Goldstein's classical mechanics to learn the Lagrangian and Hamiltonian formalisms but am concerned because I've seen threads claiming that there are serious scientific errors in the book. I can't remember the specific thread. If so can someone recommend a...

Wikipedia article under generalized forces says Also we know that the generalized forces are defined as How can I derive the first equation from the second for a monogenic system ?

Found a question on another website, I have the exact same question. Please help me Goldstein says : I do not understand how (2.34) shows that the virtual work done by forces of constraint is zero. How does the fact that "the same Hamilton's principle holds for both holonomic and...

Goldstein 3rd ed says "First consider holonomic constraints. When we derive Lagrange's equation from either Hamilton's or D'Alembert's principle, the holonomic constraint appear in the last step when the variations in the ##q_i## were considered independent of each other. However, the virtual...

I'm trying to solve the Goldstein classical mechanics exercises 1.7. The problem is to prove: $$\frac{\partial \dot T}{\partial \dot q} - 2\frac{\partial T}{\partial q} = Q$$ Below is my progress, and I got stuck at one of the step. Now since we have langrange equation: $$\frac{d}{dt}...

Are there any lecture notes that closely follow Classical Mechanics by Goldstein? I am asking this since I am seeing some comments in this forum that it contains some conceptual errors, e.g. nonholonomic constraints. If there is a book that "closely" follows Goldstein, it will be good too.

Which textbook is better for an upper division course in classical mechanics - Goldstein’s book or L&L’s book?

This is a two part question. I will write out the second part tomorrow. I will be referring to pages 258-263 in Goldstein (1965) about infinitesimal transformations. Eqn 8-66 specifies that δu=ε[u,G], where u is a scalar function and G is the generator of the transform. How do I find the...

Homework Statement Suppose the potential in a problem of one degree of freedom is linearly dependent upon time such that $$H = \frac{p^2}{2m} - mAtx $$ where A is a constant. Solve the dynamical problem by means of Hamilton's principal function under the initial conditions t = 0, x = 0, ##p =...

These images have been taken from Goldstein, Classical Mechanics. Why do we need Lagrangian formulation of mechanics when we already have Newtonian formulation of mechanics? Newtonian formulation of mechanics demands us to solve the equation of motion given by equation 1. 19. for this we need...

Can anyone tell me how if the derivative of n(n') is quadratic the second term in the taylor series expansion given below vanishes. This doubt is from the book Classical Mechanics by Goldstein Chapter 6 page 240 3rd edition. I have attached a screenshot below

is there a way for me see EVERY solution from goldstein's book? i already have some solutions, but not every one

how is md^2r/dt^2 . dr/dt = d/dt (1/2 m (dr/dt)^2 ) Thank You

When discussing about generalized coordinates, Goldstein says the following: "All sorts of quantities may be impressed to serve as generalized coordinates. Thus, the amplitudes in a Fourier expansion of vector(rj) may be used as generalized coordinates, or we may find it convenient to employ...

GreetingsTo be straight, I've been studying Goldstein Classic mechanics.While studying, it turned out that this is not a book for my level,(knew it would be challenging, but even far beyond)but even after finding out that something is wrong, i kept studying this book, by doing some research or...

currently working on format.. sor i was not preparedHi I think this question would be much related to calculus more than physics cause it seems I'd lost my way cause of calculus... but anyway! it says, Q=- \frac{\partial{U}}{\partial{q}}+\frac{d}{dt}(\frac{\partial{U}}{ \partial{ \dot{q}}} )...

I'm currently working (slowly) through Goldstein (et al), 3rd Edition, and a remark in the section on Action-angle Varibles for Completely Separable Systems (10.7) is giving me pause. We're told that the orbit equations for all ##(q_i, p_i)## pairs in phase space describe libration or periodic...

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...

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...

Hello everyone! I have a (supposedly) calculus problem that I just can't seem to figure out. Basically, I'm trying to understand why alternative kinetic energy formulation does not yield the same equations of motion in problem 11 of Goldstein's Classic Mechanics 3 edition. The text of problem...

1. The problem statement A particle moves in the ##xy## plane under the constraint that its velocity vector is always directed towards a point on the ##x## axis whose abscissa is some given function of time ##f(t)##. Show that for ##f(t)## differentiable but otherwise arbitrary, the constraint...

Homework Statement Text from a classical mechanics textbook ( uploaded picture ) shows 2 diff equation describing the motion graphically presented in the uploaded picture. How were these set up? Homework EquationsThe Attempt at a Solution I don't have a slightest clue as how are these...

Hey all, I am reading Goldstein and I am at a point where I can't follow along. He has started with D'Alembert's Principle and he is showing that Lagrange's equation can be derived from it. He states the chain rule for partial differentiation: \frac{d\textbf{r}_i}{dt}=\sum_k \frac{\partial...

On page 108 in Goldstein 3rd edition in the paragraph after equation (3.94) he says that ##\psi##` can be obtained from the orbit equation (3.36) using the limits as ##r_0=\infty## ##r=r_m## which the distance of closest approach and ##\theta_0=\pi## which is the initial direction. So looking...

I've looked at Taylor and Wheeler's Spacetime Physics Example 103 on the Thomas Precession and also the discussion of Thomas precession in Eisberg and Goldstein (3rd edition). Both treat the rotation angle gotten by the addition of 2 non-collinear velocities. The answers they get are...

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...

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})##...

Author: Herbert Goldstein (Author), Charles P. Poole Jr. (Author), John L. Safko (Author) Title: Classical Mechanics Amazon Link: https://www.amazon.com/dp/0201657023/?tag=pfamazon01-20 Prerequisities: Contents:

Hello, I have the third edition of Goldstein which I have been using to learn mechanics. I believe I have found an error in the book, however normally when I feel such things I tend to either be misreading the situation or misunderstanding the concept. I checked Professor Safko's site on...

Homework Statement In Goldstein's text, he discusses conservative fields and then states that "friction or dissipative forces are never conservative since F dot ds is always positive." From what I recall, most frictional interactions occur in directions opposite the displacement, and would...

Hi all, I like physics and I just finished Goldstein's mechanics. I don't know what my next step should be in terms of textbooks on mechanics. Also I am only a rising college sophomore, and the math I know doesn't exceed an average college sophomore too much. Does anyone have any advices as...

I apologize that this is rather specific, but hopefully enough people have used Goldstein. I have a basic grasp of action-angle variables, and I'm going through the time-independent perturbation theory section in Goldstein (12.4). In this section we seek a transformation from the unperturbed...

Classical Perturbation Theory--Time Dep. vs. Time Indep (Goldstein). Hi, I'm going through Goldstein, and I'm a little confused on the distinction between time dependent and time independent perturbation theory. In section 12.2, they do the case of a simple harmonic perturbation on force...

Homework Statement A point particle moves in space under the influence of a force derivable from a generalized potential of the form U(r, v) = V (r) + \sigma \cdot L where r is the radius vector from a fixed point, L is the angular momentum about that point, and \sigma is a fixed vector...

Homework Statement a) the lagrangian for a system of one degree of freedom can be written as. L= (m/2) (dq/dt)2sin2(wt) +q(dq/dt)sin(2wt) +(qw)2 what is the hamiltonian? is it conserved? b) introduce a new coordinate defined by Q = qsin(wt) find the lagrangian and hamiltonian...

Homework Statement I apologize if this is not the right place to put this. If it is not please redirect me for future reference. 11. Consider a uniform thin disk that rolls without slipping on a horizontal plane. A horizontal force is applied to the center of the disk and in a direction...

Homework Statement A generalized potential suitable for use in a covariant Lagrangian for a single particle U=-A_{\lambda\nu}(x_\mu)u^\lambda u^\nu where A_{\lambda\nu} stands for a symmetric world tensor of the second rank and u^\nu are the components of the world velocity. If the...

Hey, I'm looking through Goldstein's and I'm looking at equation 3.51 where it basically says \int \frac{dx}{\sqrt{\gamma x^2 + \beta x + \alpha}} = \frac{1}{\sqrt{-\gamma} } arccos \left( - \frac{\beta + 2 \gamma x}{\sqrt{\beta^2 - 4 \gamma \alpha} }\right) Every integral book I look at...

Not sure if this thread fits here, anyway. My teacher recommended this book so I decided to check it out. However, I don't really understand what to read from it. We've been doing moment of force, particle systems and static equilibrium so far. This stuff only seems to be in the first...

Hello, A question here about Classical Mechanics, Goldstein (Ed. 3) On page 87 you have expression 3.33 which goes something like \[ \frac{1}{r^2}\frac{d}{d\theta}\left(\frac{1}{mr^2}\frac{dr}{d\theta}\right)-\frac{l^2}{mr^3}=f(r) \] I appear to end up with \[...

Homework Statement From pages 124-125 in edition 3. This is about the restricted three body problem (m3 << m1,m2) http://img718.imageshack.us/img718/7012/3bdy.jpg Homework Equations L = T-V Euler-Lagrange equations The Attempt at a Solution I'm interested in m3, the...

Homework Statement (Goldstein 3.3) If the difference \psi - \omega t in represented by \rho, Kepler's equation can be written: \rho = e Sin(\omega t + \rho) Successive approximations to \rho can be obtained by expanding Sin(\rho) in a Taylor series in \rho, and then replacing \rho...

I used Marion & Thornton's Classical Dynamics of Particles and Systems for my upper division mechanics course and liked it. I want to self study Goldstein's Classical Mechanics. Are there any books that I should read before going Goldstein?

What Goldstein is to Classical Mechanics, who/m is to Quantum Mechanics?

Homework Statement (from Goldstein, problem 3.12) Suppose that there are long-range interactions between atoms in a gas in the form of central forces derivable from potential U(r) = \frac{k}{r^m}, where r is the distance between any pair of atoms and m is a positive integer. Assume further...

Problem 3 in the continuous systems and fields chapter of (the first edition, 1956 printing) of Goldstein's classical mechanics has the following Lagrangian: L = \frac{h^2}{8 \pi^2 m} \nabla \psi \cdot \nabla \psi^{*} + V \psi \psi^{*} + \frac{h}{2\pi i} ( \psi^{*} \dot{\psi} - \psi...

Question: Analyze the motion of a small bead attached to a wire which is rotating along a fixed axis? Proof(Using Lagrangian formulation): Clearly here the generalized coordinate is the distance of the particle along the wire. so we have the formulae \frac{d \frac{\delta T}{\delta r}}{dt} -...

Can someone Prove the thing in bold letters?

i don't get this what he wrote... the internal force \vec{F_{ij}} between two particles is \vec{F_{ij}}=\nabla_{i} V_{ij}=\nabla_{ij} V_{ij}=-\nabla_{j} V_{ij} where the subscript below \nabla_{k}implies the differentitaion with respect to components of \vec{r_{k}} i can't get how...