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9 Variational Principles in Mechanics and Their Applications
O
k
m
Problem 9.5 Mass-spring system
O
k 1
k 2
m 1
m 2
y 10
y 1
y 20
y 2
Problem 9.6 The choice of coupled spring coordinates
and the friction force of motion is negligible, find the differential equation of
motion of the two objects when the system is under the action of gravity.
9.12 As shown in Problem 9.7, a homogeneous circular cylinder that the radius is
r, the mass is m makes pure rolling within the cylindrical groove of radius R,
using the Hamilton’s principle to derive the equation of small vibration and
period of vibration of the circular cylinder.
9.13 As shown in Problem 9.8, find the differential equation of motion of a spherical
pendulum of length L.
9.14 A particle of mass m can frictionlessly slide in a circular small tube of radius
r. The small tube rotates at the steady angular velocity ω around the vertical
9 Variational Principles in Mechanics and Their Applications
O
k
m
Problem 9.5 Mass-spring system
O
k 1
k 2
m 1
m 2
y 10
y 1
y 20
y 2
Problem 9.6 The choice of coupled spring coordinates
and the friction force of motion is negligible, find the differential equation of
motion of the two objects when the system is under the action of gravity.
9.12 As shown in Problem 9.7, a homogeneous circular cylinder that the radius is
r, the mass is m makes pure rolling within the cylindrical groove of radius R,
using the Hamilton’s principle to derive the equation of small vibration and
period of vibration of the circular cylinder.
9.13 As shown in Problem 9.8, find the differential equation of motion of a spherical
pendulum of length L.
9.14 A particle of mass m can frictionlessly slide in a circular small tube of radius
r. The small tube rotates at the steady angular velocity ω around the vertical