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Gang Sheng Chen (Gang Sheng, Gang Chen), Ph.D.
Mechanical Engineering Department
University of Alaska Fairbanks
ME 608ME 608
Advanced DynamicsAdvanced Dynamics(lectures 2)(lectures 2)
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Advanced Dynamics
Contents
Review of dynamics (ES210)
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Course content ofES 210 (according to syllabus)
Review of dynamics ES 210
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Review of Dynamics (chapters 13-17)
Acceleration vs. Force: Newtons second law of motion
The acceleration ofan object is directly proportional to the net
force acting on it and inversely proportional to its mass
txmtF !
Workdone by a varying force dxtFW !
Kinetic energy ofmoving mass ? A22
1txmEk !
Potential energy ofcompressed spring ? A22
1txkEp !
mtFtx /
! or
Applied to particle model
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Work vs. Energy:Work-energy theorem:the workdone by force (applied on mass orspring) equals the change in
energy (mass orspring)EWnet (!
Gravitational potential energy ofmass above ground H
mgHEg !
Work vs. Energy: Conservation of energy
Under
th
e eff
ectof
co
nservative
forces
gfsfkfgisiki EEEEEE !
Review of dynamics
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Impulse vs. Momentum: Collisions
Impulse offorce equals to the change in momentum ofbody
Linearmomentum
Conservation ofmomentum
ifa closed system is not affected by external forces
txmp ! pdttFI (!!
ffii pppp 2121 !
Review of dynamics
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Rotational energy ofbody 2
2
1 [IEr !
Mass moment of inertia dVrdmrI !!22
V
Workand energy in rotational motion
rirf
EETdW !! U
Net external torque vs. angularacceleration
ttt
tItT
U[E
E
!!
! ,
Parallel axis theorem 20 mRII !
Angularacceleration
Review of dynamics
Dynamics of a Rigid Body (to fixed point)
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Kinetic Energy ofa rigid body in Rolling motion
22
22
22
])[(2
1
][2
1][
2
1
2
1][
2
1
txr
Im
r
txItxm
ItxmEr
!
!!
!! [
Review of dynamics
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Review of dynamics ES 210
Chapter 18: 2D dynamics of a rigid body
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This can be reduced to (notes):
IfP is the same point as G, then :
Review of dynamics ES 210
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Review of dynamics ES 210
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Can be reduced to (notes):
Equation:
Review of dynamics ES 210
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This can also be expressed in
terms
ofinstantane
ous cente
r
ofzero velocity:
Review of dynamics ES 210
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Review of dynamics ES 210
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Review of dynamics ES 210
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Work
of
a Weigh
t
Review of dynamics ES 210
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Workofa Spring Force
Review of dynamics ES 210
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Forces That DoNoWork:N, Ff, and W
Review of dynamics ES 210
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Review of dynamics ES 210
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Review of dynamics ES 210
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Review of dynamics ES 210
Advanced Dynamics---Beyond above dynamics:
From 2D to 3D
From one body to multiple bodies
From Newtonian formulation to Lagrange and
Hamilton formulations
Vibrations
Multidisciplinary engineering applications