6.19. Double pendulum **** Consider a double pendulum made of two masses, m₁ and m2, and two rods of lengths ₁ and 2 (see Fig. 6.22). Find the equations of motion. For small oscillations, find the normal modes and their frequencies for the special case 1 = l2 (and consider the cases m₁ = m2,m1 » m2, and m₁ m₂). Do the same for the special case m₁ = m2 (and consider the cases l1l2, l1 » l2, and l₁ << l₂). Fig. 6.22 m1 11 m2
6.19. Double pendulum **** Consider a double pendulum made of two masses, m₁ and m2, and two rods of lengths ₁ and 2 (see Fig. 6.22). Find the equations of motion. For small oscillations, find the normal modes and their frequencies for the special case 1 = l2 (and consider the cases m₁ = m2,m1 » m2, and m₁ m₂). Do the same for the special case m₁ = m2 (and consider the cases l1l2, l1 » l2, and l₁ << l₂). Fig. 6.22 m1 11 m2
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Transcribed Image Text:6.19. Double pendulum ****
Consider a double pendulum made of two masses, m₁ and m2, and two
rods of lengths ₁ and 2 (see Fig. 6.22). Find the equations of motion.
For small oscillations, find the normal modes and their frequencies
for the special case li = l2 (and consider the cases m₁ = m2,m1 >> m2,
and m₁ m₂). Do the same for the special case m₁ = m₂ (and consider
the cases l1l2, l1 » l2, and l₁ << l₂).
Fig. 6.22
m1
41
m2
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