A flyball governor for a steam engine consists of two balls, each of mass m, attached by means of four hinged arms, each of length 1, to sleaves located on a vertical rod. The lower sleeve has mass M and negligible moment of inertial, and is free to slide up and down the rod without friction. The upper sleeve is fastened to the rod. The system is constrained to rotate with constant angular velocity w. (a) Choose suitable coordinates and write the Hamilto- nian functions for the system. Neglect weights of arms and rod, and neglect friction.
A flyball governor for a steam engine consists of two balls, each of mass m, attached by means of four hinged arms, each of length 1, to sleaves located on a vertical rod. The lower sleeve has mass M and negligible moment of inertial, and is free to slide up and down the rod without friction. The upper sleeve is fastened to the rod. The system is constrained to rotate with constant angular velocity w. (a) Choose suitable coordinates and write the Hamilto- nian functions for the system. Neglect weights of arms and rod, and neglect friction.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Transcribed Image Text:A flyball governor for a steam engine consists of two balls, each of mass
m, attached by means of four hinged arms, each of length 1, to sleaves
located on a vertical rod. The lower sleeve has mass M and negligible
moment of inertial, and is free to slide up and down the rod without friction.
The upper sleeve is fastened to the rod. The system is constrained to rotate
with constant angular velocity w.
(a) Choose suitable coordinates and write the
Hamilto
nian functions for the system. Neglect weights of arms and rod, and neglect
friction.
Pa
ml²² sin² 0-2(m + M)gl sin 8
H =
-ml²w² sin² 0-2(m+M)gl sin 0
4(m+2M sin² @)²
4(m-2M sin 1²
Option 1
Option 2
O
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