Question

8.9 A chain of mass m and length / lies on a horizontal table with a portion hanging over the edge of the table. The only force acting on the system is the constant gravitational force in the negative y-direction. Set up and solve Lagrange's equation. Assume uniform mass density. 8.10 (a) Set up Lagrange's equations for the double pendulum (see Figure 8.8). (b) Assume that the amplitudes are very small. Simplify the equations keeping only terms linear in the variables.

8.9.) A chain of mass m and length l lies on a horizontal table with a portion hanging over the edgeof the table. The only force acting on the system is the constant gravitational force in the negative y- direction. Set up and solve Lagrange's equation. Assume uniform mass density.
8.10.) a) Set up Lagrange's equations for the double pendulum (Figure 8.8).
b) Assume that the amplitudes are very small. Simplify the equations keeping only terms linear in the variables.

The third picture is the answers to the problems according to the textbook

Answer 1

cartesian Cosdinates of m, & my are ! LX,y),=sing, -l4os). (4,4)=(4 sine, th sine,-lqces8;=blo102) to to tado-Ot V = -mgy=My gyz d= T-V %3D tmightlosetmgA,Less_thles&).

simülasly for O IM2J&sinOz upfying-theuations Reeping the leading orda terms. D=(M,+m) ot M&ô7(m,+M)g8 0.
There is a small error in the solution given in the attachment I have checked my answer from other books as well.