9.11 Introduction to the Famous Scientists
607
Problem 9.12 Plane
pendulum
O
m 1
m 2
R
ϕ
another small ball of mass m 2 smoothly fits over the swinging link, it can both
slide freely along the swing link, and can slide in the fixed cylindrical groove
of radius R, the friction is neglected. Write the differential equation of motion
of the system with the Hamilton’s principle.
9.18 The suspension point of a simple pendulum can overcome the elastic restoring
force frictionlessly sliding along the horizontal line, as shown in Problem 9.13.
Let x be the horizontal displacement of the suspension point, and θ is the angle
of the pendulum and vertical line, Find the differential equations of motion of
the system with the Lagrange equation.
9.19 Find the Hamiltonian form of Euler equations of the functional J =
x 1
x 0
x y
√
y dx.
Problem 9.13 Springsimple
system
k
k
l
m
θ
607
Problem 9.12 Plane
pendulum
O
m 1
m 2
R
ϕ
another small ball of mass m 2 smoothly fits over the swinging link, it can both
slide freely along the swing link, and can slide in the fixed cylindrical groove
of radius R, the friction is neglected. Write the differential equation of motion
of the system with the Hamilton’s principle.
9.18 The suspension point of a simple pendulum can overcome the elastic restoring
force frictionlessly sliding along the horizontal line, as shown in Problem 9.13.
Let x be the horizontal displacement of the suspension point, and θ is the angle
of the pendulum and vertical line, Find the differential equations of motion of
the system with the Lagrange equation.
9.19 Find the Hamiltonian form of Euler equations of the functional J =
x 1
x 0
x y
√
y dx.
Problem 9.13 Springsimple
system
k
k
l
m
θ