→ 252/7.10 (MT): A particle of mass m starts at rest on top of a smooth fixed hemisphere of radius a. Find the force of constraint, and determine the angle angle at which the at which the particle leaves the hemisphere.
→ 252/7.10 (MT): A particle of mass m starts at rest on top of a smooth fixed hemisphere of radius a. Find the force of constraint, and determine the angle angle at which the at which the particle leaves the hemisphere.
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Transcribed Image Text:10:50
← Ch-5_Lagrangian...
Example
A
252/7.10 (MT): A particle of mass m starts at rest on top of a smooth
fixed hemisphere of radius a. Find the force of constraint, and determine
the angle at which the particle leaves the hemisphere.
e angle at which the
AGH
AGH
Example
→ 447/10.7.1: Consider a disk with mass m,
radius R, and moment of inertia I = mR².
e fick has a profes
The disk has a string wrapped around it
with one end attached to a fixed support
and allowed to fall with the string
unwinding as it falls. Find the equations of
motion of the falling disc and the forces of
constraint.
AGH
5-Hamiltonian Dynamics
A
Closed system → can not depend explicitly on time → / at = 0
dL (ƏL dqi
ƏL dài
cai ,t) = L(qi, ġi)
=
dt
aqi dt
əqi dt
Recall
|||
al d ƏL
Đại dt\Đài,
= 0⇒>
ас
əqi
=
AGH
24/33
+
87%
d (al
dt aq
囧
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