Consider the pendulum x' Y, y' = -vy - sinx, - where 0 is a friction parameter and (x, y) E S¹ x R where we view the circle S¹ to be the interval [-T, π] with the boundaries identified. Show that for v = = 0, the system is Hamiltonian by constructing a Hamilton function H.
Consider the pendulum x' Y, y' = -vy - sinx, - where 0 is a friction parameter and (x, y) E S¹ x R where we view the circle S¹ to be the interval [-T, π] with the boundaries identified. Show that for v = = 0, the system is Hamiltonian by constructing a Hamilton function H.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
H2.
![Consider the pendulum
x'
y = -vy- sinx,
-
Y,
where v≥ 0 is a friction parameter and (x, y) € S¹ x R where we view the circle S¹ to be
the interval [-T, π] with the boundaries identified.
Show that for v = 0, the system is Hamiltonian by constructing a Hamilton function
H.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fad4a1d8a-f714-48d4-9f8e-5ca7c5c9633b%2F25a2e9d2-6f40-4796-a2f9-175a773072ea%2Frnueri_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the pendulum
x'
y = -vy- sinx,
-
Y,
where v≥ 0 is a friction parameter and (x, y) € S¹ x R where we view the circle S¹ to be
the interval [-T, π] with the boundaries identified.
Show that for v = 0, the system is Hamiltonian by constructing a Hamilton function
H.
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