Goldstein Definition and 56 Threads

Baruch Kopel Goldstein (Hebrew: ברוך קופל גולדשטיין‎; born Benjamin Goldstein; December 9, 1956 – February 25, 1994) was an American-Israeli mass murderer, religious extremist, and physician who perpetrated the 1994 Cave of the Patriarchs massacre in Hebron, killing 29 and wounding 125 Palestinian Muslim worshippers. He was beaten to death by survivors of the massacre.The Israeli government condemned the massacre, and responded by arresting followers of Meir Kahane, criminalizing the Kach movement and affiliated movements as terrorist, forbidding certain Israeli settlers to enter Palestinian towns, and demanding that those settlers turn in their army-issued rifles, although rejecting a Palestinian Liberation Organization demand that all settlers in the West Bank be disarmed and that an international force be created to protect Palestinians.Jewish Israelis were barred from entering major Arab communities in Hebron. The Israeli government also took extreme measures against Palestinians following the deadly riots after the massacre, expelling them from certain streets near Jewish settlements in Hebron, such as Al-Shuhada Street, where many Palestinians had homes and businesses, and allowing access exclusively to Jewish Israelis and foreign tourists.Goldstein's gravesite became a pilgrimage site for Jewish extremists. The following words are inscribed on the tomb: "He gave his life for the people of Israel, its Torah and land." In 1999, after the passing of Israeli legislation outlawing monuments to terrorists, the Israeli Army dismantled the shrine that had been built to Goldstein at the site of his interment. The tombstone and its epitaph, calling Goldstein a martyr with clean hands and a pure heart, was left untouched. After the flagstones around it were pried away under the eye of a military chaplain, the ground was covered with gravel.

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  1. jv07cs

    Why is Hamilton's Principle assumed to be valid for non-holonomic systems?

    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...
  2. Falgun

    Classical Are There Scientific Errors in Goldstein's Classical Mechanics?

    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...
  3. K

    A Two equations of generalized forces

    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 ?
  4. K

    A Hamilton's principle and virtual work by constraint forces

    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...
  5. K

    I Virtual displacement is not consistent with constraints

    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...
  6. L

    I Help with Goldstein Classical Mechanics Exercise 1.7

    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}...
  7. S

    Classical Supplement to Classical Mechanics by Goldstein

    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.
  8. J

    Classical Classical Mechanics: Landau vs Goldstein Textbooks

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

    Generators of infinitesimal transforms from Goldstein (1965)

    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...
  10. D

    Hamilton Jacobi equation for time dependent potential

    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 =...
  11. Pushoam

    Why do we need the Lagrangian formulation of Mechanics?

    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...
  12. Ben Geoffrey

    I Taylor Series Expansion of Quadratic Derivatives: Goldstein Ch. 6, Pg. 240

    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
  13. U

    Classical Goldstein 3ed Classical mechanics solutions

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

    How Does Goldstein Derive the Kinetic Energy Equation in Classical Mechanics?

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

    I Amplitudes of Fourier expansion of a vector as the generalized coordinates

    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...
  16. R

    Studying Requirement for Goldstein level Classic mechanics

    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...
  17. R

    Question from Velocity-Dependent Potential in lagrangian (Goldstein)

    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}}} )...
  18. C

    I Goldstein Action-angle Variables

    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...
  19. N

    Classical What Is the Best Path to Tackle Goldstein's Classical Mechanics?

    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...
  20. avorobey

    Mass hanging under a table: a problem from Goldstein

    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...
  21. Fedor Indutny

    B Alternative Kinetic Energy Formulation and Goldstein's Problem 11

    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...
  22. D

    Goldstein Derivation 1.6: Nonholonomic Constraints in Particle Motion

    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...
  23. D

    Motion described by differential equations

    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...
  24. C

    A Question on Goldstein and D'Alembert's Principle

    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...
  25. D

    Goldstein Central Force Repulsive Scattering

    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...
  26. G

    Thomas precession Goldstein/Eisberg versus Taylor/Wheeler

    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...
  27. J

    Goldstein Mechanics example motion of one particle in polar coordinates

    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...
  28. P

    Classical Mechanics Goldstein 2.16

    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})##...
  29. Greg Bernhardt

    Classical Classical Mechanics by Herbert Goldstein

    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:
  30. M

    Is There a Mistake in Goldstein's Mechanics on Cos Theta Definition?

    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...
  31. S

    Goldstein classical mechanics discrepancy?

    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...
  32. B

    What's the Next Step in Mechanics After Goldstein?

    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...
  33. B

    Specific question on Goldstein section on Time-independent perturbation theory

    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...
  34. B

    Classical Perturbation Theory-Time Dep. vs. Time Indep (Goldstein).

    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...
  35. D

    Goldstein Mechanics chpt 1, Exercise 15

    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...
  36. L

    Lagrangian hamiltonian mech COC Goldstein 8.27

    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...
  37. D

    Mechanics Goldstein, chpt 1 exercise 11, Lagrangian of rolling disk

    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...
  38. Q

    Asking for hints to Goldstein chapter 7, problem 9

    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...
  39. maverick_starstrider

    Trouble with a line in Goldstein

    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...
  40. I

    Goldstein - CM - chapter guidance?

    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...
  41. G

    Differential Equation for the Orbit - Goldstein Chapter 3

    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 \[...
  42. C

    Help with example from goldstein (lagrangian)

    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...
  43. B

    Solving Goldstein 3.3: Taylor Series & Newton-Rhapson

    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...
  44. W

    Learn Classical Mechanics: Prerequisites for Goldstein's Book

    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?
  45. W

    Exploring Quantum Mechanics: Who is the Goldstein of QM?

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

    Gas with interacting molecules (from goldstein)

    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...
  47. Peeter

    Goldstein schodinger's equation Lagragian problem.

    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...
  48. P

    Explain the proof in goldstein

    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} -...
  49. P

    Classical Mech doubt 4m Goldstein

    Can someone Prove the thing in bold letters?
  50. P

    Why is Mechanics Goldstein difficult to understand?

    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...
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