Classical Dynamics : A Contemporary Approach. Recent advances in the study of dynamical systems have revolutionized the way that classical mechanics is taught and understood. This new and comprehensive textbook provides a complete description of this fundamental branch of physics. The authors cover all the material that one would expect to find in a standard graduate course: Lagrangian and Hamiltonian dynamics, canonical transformations, the Hamilton-Jacobi equation, perturbation methods, and rigid bodies.

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Compartir este documento Compartir o incrustar documentos Opciones para compartir Compartir en Facebook, abre una nueva ventana Facebook. Denunciar este documento. Descargar ahora. Carrusel Anterior Carrusel Siguiente. Solved Problems of Jackson's Electrodynamics Jackson Solutions - Solutions to jackson's Electrodynamics. Goldstein H. Solutions Classical Dynamics of Particles and Systems 5ed.

Buscar dentro del documento. We would also be grateful for other problems with solutions that we conld put on a web site without the solutions. With yonr consent we would give yon credit for any problems used.

Please be aware that the manual is for your use only; please handle it discreetly, We are anxious not to have it circulate widely, for if it were to become available to students, the problem sets in the book would be nseless as learning tools.

Please do not share it in its entirety with graduate-student graders, to whom you may want to give the solutions to specific assigned problems. We count on your care in this matter. A technique we have used, imperfect though itt is, has been to post answers to assigned problems on a website for a limited period say a week. For any questions or suggestions you can reach us at onr E-mail addresses: jiv neu.

A gun is mounted on a hill of height h above a level plane. Neglecting air resistance, find the angle of elevation a for the greatest horizontal range at a given muzzle speed v.

Find this range. Note cos? Problem 2. The plane itself is on rollers and is free to move horizontally, also without frietion; it has mass M. Pind the acceleration A of the plane and the acceleration a of the mass m.

Forces on the mass rm; mg downward and the normal force NV of the ramp. Forees on M : The reaction to the normal force on mt, also of magnitude N. Also gravitational force and vertical force from the ground, which we ignore. The student should draw free-body diagrams. Three equations, four unknowns W,a2,4y,A.

For velocities, ete. Do some algebra and take derivatives w. Take it from there. Problem 3. Figures 1. In all four cases find the acceleration A of the center of mass and the angular acceleration a of the cylindrical object; show explicitly that the work-energy theorem is satisfied. The string passes through the center of mass of the cylinder. How does the hand manage to supply the necessary translational and kinetic energies different, from Part c?

That Jat? But is doer no werk rince the energy i equal to the work done oy tbe band Explanation: the bottom point is instantaneously at rest, a pivot. If there were no friction, the bottom of the cylinder would move accelerate to the left. Again, iction does no work. A particle of mass m makes an elastic kinetic-energy conserving collision with another particle of mass Before the collision my has velocity v1 and rig is at rest relative to a certain inertial frame which we shall call the laboratory system.

After the collision m, has velocity uy making an angle with vy. Find the velocity of the center-of-mass system relative to the laboratory system. Problem 5. Set up a suitable coordinate system and describe the subsequent motion of my and mp Solution. The Earth and the Moon form a two-body system interacting through their mutual gravitational attraction.

Take the Sumas the origin and write down the equations of motion for the center of mass X and the relative position x of the Barth-Moon system.

From di- Tyy — Fe. GmX [3 cee eareoxe [i TMX? Problem 8. A yo-yo consists of two disks of mass M and radius R connected by a shaft of mass m and radius r; a weightless string is wrapped around the shaft. Assuming that the string starts out vertical, find the motion of the yo-yo's center of mass. Describe the motion of the free end of the string and the rotation of the yo-yo. Describe the motion of the center of mass of the yoryo, the yo-yo's rotation, and the motion of the free end of the string.

Check it out. The free end of the string his can also be checked by equivalence. Problem 9. Find the general solution to the equations of motion and show that the velocity hes an asymptotic value called the terminal velocity. Find the terminal velocit Solution, Answer in just one dimension. Notes: 1. Change the variable of integration in Hq, I. Show that what Eq. Problem A particle is constrained to move at constant speed on the ellipse ayer? Pind the Cartesian components of its acceleration as a function of position on the ellipse.

It is directed normal to the curve. They all check. We let it go at that. Show that if B4. Consider Hq. Give the physical significance of the terms you obtain.

A particle of mass m moves in one dimension under the influence of the force Pater F Find the equilibrium points, show that they are stable, and calculate the frequencies of oscillation about them. Show that the frequencies are independent of the energy. With the force given, Vey tate The graphs shows V z solid curve. In this system the peri independent of frequency in the large.

This is a rare example of a nonlinear system whose frequency is independent of amplitude. Here is a tricky way to do this problem. Show that the center of mass of the entire system is given by an equation similar to 1. A simple understanding of this: In a continuous distribution replace each my by din x at various points x.

Then 1 becomes the position y x of the point x with respect to the center of mass, and mag? The second term in the discrete-syster result. In deriving Eq. Show explicitly that if for each and j the internal force Fy lies along the line connecting the ith ond jth particles, then the internal forces indeed do not contribute to the total torque. Draw the phase portrait for a particle in a uniform gravitational ficld. Make this a system of one freedom by considering motion only in the vertical direction Solution.

Pind the equilibrium points of the motion, draw f rough graph of the potential, and draw the phase portrait of the system. On these graphs indicate the relation between the energy and geometry of the phase-space orbits, Solution. The center of the phase portrait corresponds to the central rinimum in the graph of V.

The curves running off to the right and the left do not close: they become asyraptotic to horizontal straight lines. Draw the phase portrait for the system of Problem The graph of the potential is shown in the answer to Problem Draw the phase portrait for a particle in a uniform grevitational field with a velocity-dependent retarding force the same as the one in Problem 9.

Consider motion only in the vertical direction Solution. Positive is downward in the direction of g. At large positive and negative values of v the slopes are all the same, both above and below the 2 axis Problem the mass to rise from B to the turning point at hy and to descend again assume it was moving to the right at B.


Solutions Manual - Classical Dynamics, Jose, Saletan

Embed Size px x x x x We want to present you with a modern course in classical dynamics, Jos and E. Introduction to Classical Dynamics


Jose, Saletan. Classical Dynamics

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