- 7.7.1: Write down the Lagrangian for a projectile (subject to no air resis...
- 7.7.2: Write down the Lagrangian for a one-dimensional particle moving alo...
- 7.7.3: Consider a mass in moving in two dimensions with potential energy U...
- 7.7.4: Consider a mass m moving in a frictionless plane that slopes at an ...
- 7.7.5: Find the components of V f (r, 0) in two-dimensional polar coordina...
- 7.7.6: Consider two particles moving unconstrained in three dimensions, wi...
- 7.7.7: Do 7.6, but for N particles moving unconstrained in three dimension...
- 7.7.8: (a) Write down the Lagrangian L (x1, x2, xl, i2) for two particles ...
- 7.7.9: Consider a bead that is threaded on a rigid circular hoop of radius...
- 7.7.10: A particle is confined to move on the surface of a circular cone wi...
- 7.7.11: Consider the pendulum of Figure 7.4, suspended inside a railroad ca...
- 7.7.12: ?Lagrange's equations in the form discussed in this chapter hold on...
- 7.7.13: In Section 7.4 [Equations (7.41) through (7.51)], I proved Lagrange...
- 7.7.14: Figure 7.12 shows a crude model of a yoyo. A massless string is sus...
- 7.7.15: A mass mi rests on a frictionless horizontal table and is attached ...
- 7.7.16: Write down the Lagrangian for a cylinder (mass m, radius R, and mom...
- 7.7.17: Use the Lagrangian method to find the acceleration of the Atwood ma...
- 7.7.18: A mass m is suspended from a massless string, the other end of whic...
- 7.7.19: In Example 7.5 (page 258) the two accelerations are given by Equati...
- 7.7.20: A smooth wire is bent into the shape of a helix, with cylindrical p...
- 7.7.21: The center of a long frictionless rod is pivoted at the origin, and...
- 7.7.22: Using the usual angle 0 as generalized coordinate, write down the L...
- 7.7.23: A small cart (mass m) is mounted on rails inside a large cart. The ...
- 7.7.24: We saw in Example 7.3 (page 255) that the acceleration of the Atwoo...
- 7.7.25: Prove that the potential energy of a central force F = krni (with n...
- 7.7.26: In Example 7.7 (page 264), we saw that the bead on a spinning hoop ...
- 7.7.27: Consider a double Atwood machine constructed as follows: A mass 4m ...
- 7.7.28: A couple of points need checking from Example 7.6 (page 260). (a) F...
- 7.7.29: ?Figure 7.14 shows a simple pendulum (mass m, length l) whose point...
- 7.7.30: Consider the pendulum of Figure 7.4, suspended inside a railroad ca...
- 7.7.31: A simple pendulum (mass M and length L) is suspended from a cart (m...
- 7.7.32: Consider the cube balanced on a cylinder as described in Example 4....
- 7.7.33: A bar of soap (mass m) is at rest on a frictionless rectangular pla...
- 7.7.34: Consider the well-known problem of a cart of mass m moving along th...
- 7.7.35: Figure 7.16 is a bird's-eye view of a smooth horizontal wire hoop t...
- 7.7.36: A pendulum is made from a massless spring (force constant k and uns...
- 7.7.37: Two equal masses, ml = m2 = m, are joined by a massless string of l...
- 7.7.38: A particle is confined to move on the surface of a circular cone wi...
- 7.7.39: a) Write down the Lagrangian for a particle moving in three dimensi...
- 7.7.40: The "spherical pendulum" is just a simple pendulum that is free to ...
- 7.7.41: Consider a bead of mass m sliding without friction on a wire that i...
- 7.7.42: [Computer] In Example 7.7 (page 264), we saw that the bead on a spi...
- 7.7.43: Computer] Consider a massless wheel of radius R mounted on a fricti...
- 7.7.44: [Computer] If you haven't already done so, do 7.29. One might expec...
- 7.7.45: (a) Verify that the coefficients Ai j in the important expression (...
- 7.7.46: Noether's theorem asserts a connection between invariance principle...
- 7.7.47: In Chapter 4 (at the end of Section 4.7) I claimed that, for a syst...
- 7.7.48: Let F = F (q 1, , qn) be any function of the generalized coordinate...
- 7.7.49: Consider a particle of mass in and charge q moving in a uniform con...
- 7.7.50: A mass m1 rests on a frictionless horizontal table. Attached to it ...
- 7.7.51: Write down the Lagrangian for the simple pendulum of Figure 7.2 in ...
- 7.7.52: The method of Lagrange multipliers works perfectly well with non-Ca...
Solutions for Chapter 7: Lagrange's Equations
Full solutions for Classical Mechanics | 0th Edition
ISBN: 9781891389221
Solutions for Chapter 7
23
2
Summary of Chapter 7: Lagrange's Equations
The theoretical development of the laws of motion of bodies is a problem of such interest and importance that it has engaged the attention of all the most eminent mathematicians since the invention of dynamics as a mathematical science by Galileo, and especially since the wonderful extension which was given to that science by Newton.
This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Classical Mechanics, edition: 0. Classical Mechanics was written by and is associated to the ISBN: 9781891389221. Chapter 7: Lagrange's Equations includes 52 full step-by-step solutions. Since 52 problems in chapter 7: Lagrange's Equations have been answered, more than 158515 students have viewed full step-by-step solutions from this chapter.
Key Physics Terms and definitions covered in this textbook
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parallel
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any symbol
average (indicated by a bar over a symbol—e.g., v¯ is average velocity)
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°C
Celsius degree
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°F
Fahrenheit degree