8/3/2019 ME 608 notes 2 2012

1/21

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)

8/3/2019 ME 608 notes 2 2012

2/21

Advanced Dynamics

Contents

Review of dynamics (ES210)

8/3/2019 ME 608 notes 2 2012

3/21

Course content ofES 210 (according to syllabus)

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

4/21

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

8/3/2019 ME 608 notes 2 2012

5/21

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

8/3/2019 ME 608 notes 2 2012

6/21

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

8/3/2019 ME 608 notes 2 2012

7/21

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)

8/3/2019 ME 608 notes 2 2012

8/21

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

8/3/2019 ME 608 notes 2 2012

9/21

Review of dynamics ES 210

Chapter 18: 2D dynamics of a rigid body

8/3/2019 ME 608 notes 2 2012

10/21

This can be reduced to (notes):

IfP is the same point as G, then :

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

11/21

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

12/21

Can be reduced to (notes):

Equation:

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

13/21

This can also be expressed in

terms

ofinstantane

ous cente

r

ofzero velocity:

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

14/21

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

15/21

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

16/21

Work

of

a Weigh

t

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

17/21

Workofa Spring Force

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

18/21

Forces That DoNoWork:N, Ff, and W

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

19/21

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

20/21

Review of dynamics ES 210

8/3/2019 ME 608 notes 2 2012

21/21

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