Dynamics
P Kim (Chonbuk National University) Undergraduate course, 2nd year 1
Dynamics
Kim Pilkee
School of Mechanical Design Engineering
Jeonbuk National University, Republic of Korea
E-mail: [email protected]
Tel: 063-270-4755
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Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year^
Dynamics^ Kim Pilkee
School of Mechanical Design EngineeringJeonbuk National University, Republic of Korea
E-mail: [email protected]: 063-270-
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year^
Dynamics (
th^ ed.), J.L. Meriam, Wiley
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year^
Chapter 1Introduction to Dynamics
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Introduction to Dynamics
Basic Concepts I
Basic Concepts
^ Kinematics
&^ Kinetics
Statics 1) Statics deals with the effects of forces on bodies
at rest
.^ ^ static deflection
Dynamics 1) Dynamics deals with the
motion of bodies
under the action of forces.
^ displacement,velocity, acceleration
Kinematics 1) Kinematics is the study of motion
without reference to the forces
which cause motion.
Kinetics 1) Kinetics relates the
action of forces on bodies to their resulting motions
.
(1/2)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Introduction to Dynamics
Basic Concepts III
Basic Concepts
Q) An airplane system’d better be considered as a particle or a rigid body?
(Air flow)
(Stress distribution)
(Wing deflection)
Airplane Designs
(1/2)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Introduction to Dynamics
Basic Concepts IV
Basic Concepts
Space 1)^ Space
is the geometric region occupied by bodies. 2)^ Position
in space is determined relative to some geometric reference system by means of linear^ and
angular
measurements.
Frame of Reference 1) Newtonian mechanics is based on
primary inertial reference
or^ astronomical frame of
reference
, which is an imaginary set of rectangular axes assumed to have
no translation or
rotation
in^ space
. ^ Rectangular (=perpendicular=orthogonal)
axes or coordinates
O
Point O: origin of coordinatePoint A: particle
Vector & Scalar 1)^ Vector
: direction & magnitude 2)^ Scalar
: magnitude
(1/2)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Introduction to Dynamics
^ Weight^ W^
mg
^ Effect of a Rotating Earth ^ Standard Value of g (=9.806 m/s
2 )
: gravitational acceleration relative to the rotating earth at sea level and at a latitude of 45
°
Newton’s Laws & Gravitation II
Newton’s Laws & Gravitation
Gravitation (cont.)
(1/3) (1/5)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Introduction to Dynamics
Dimensions & Units
Dimensions & Units
Dimensions 1.^ [Math]
Dimension of a vector space = Number of basis vectors (e.g., 1-D, 2-D, or 3-D space)
2.^ [Physics]
Dimension of a physical quantity (e.g., length, area, volume, time, mass, or force)
- A^ physical dimension
is different from a
unit^ and can be expressed in a number of different
^ Physical Quantities [Dimensions]: Length [L], Mass [M], Time [T] ^ Composite Physical Dimensions: Force [F]=[ML/T units (e.g., meters, millimeters, or kilometers for length).
2 ], Velocity [L/T], Acceleration [L/T
2 ]
^ Principle of dimensional homogeneity:^ The dimensions of all terms in an equation must be the same. Units
(1/4) (1/6)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Kinematics of Particles
Choice of Coordinates Coordinate Systems1. [2-D space] ^ Rectangular coordinates (
x-y ):
^ Polar coordinate
( r-θ ):
, i j
, e e r^
2. [3-D space]^ ^ Rectangular coordinates (
x-y-z ):
^ Cylindrical coordinate
( r-θ-z ):
^ Spherical coordinate
( R-θ-ϕ
, , i j k , ):
, e e k r , , e e e R
3. [Path coordinate system]^ ^ Normal-tangential coordinates:
, e^ e n^ t
Choice of Coordinates
(2/1)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Kinematics of Particles
Rectilinear Motion I
Rectilinear Motion
Rectilinear Motion 1. Rectilinear motion (or
straight-line motion
) is the simplest motion of a particle or a body
travelling along a straight line on space.2. Especially for a particle, rectilinear motion can be described with the simplest 1-D coordinatesystem which is called ‘
Number Line
’ like a ruler.
^ Rectilinear Motion of a Particle
^ Rectilinear Motion of a Rigid Body
^ Number Line: the direction of motion can be expressed with a plus or minus sign. ^ Number Line: 1-D vector space (≠ scalar)
(2/2)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Kinematics of Particles
Rectilinear Motion III
Rectilinear Motion
[Differential Equations]
for the rectilinear motion of a particle 2 2
i)
iii)^
or
ii)^
or dsv s dt^
vdv^ ads
sds
sds
dv^
d s a^
v^ a^
s dt^
dt
^ ^
^
^
^
^ ^
^
^
^
(Note) Derivative Notations^ ^
= difference
b/w the values of
x
^ = infinitesimal change
in^ x
^ =
( derivative of
y^ with respect to
x )^ =^ ( ratio
of two infinitesimal quantities,
dx^ &^ dy
)
dx dx dy
(dot) time derivative,
(prime) spatial derivative
dx^
dx
x^
x
dt^
ds
^ ^
^
x
^ no time is involved.
(2/2)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Kinematics of Particles
Rectilinear Motion IV
Rectilinear Motion
Analytical Integration 1.^ If the relationship between position coordinate and time is unknown
, then it must be
determined by successive integration from the acceleration.2.^ [Constant Acceleration]
i)^
,^ ii)^
,^ iii) ds^
dv v^
a^
vdv^ ads dt^
dt ^
^
^ Differential Equations
^
^
^ 0 0
0
0
0
0
0
0
0 0
2
0
0
0
0
2
v^
t^
v^
t v v
t
s^
t^
s s
s
v
v^
s^
s s
v^
s^
v
dva
dv^ adt
dv^ a^
dt^
v^ a t
dt dsv ds
vdt^
ds^
v^ at dt
s
v t
at
dt vdv ads^
vdv^ a ds^
v^
a s
^ ^
^
^
^
^ ^
^
^
^ ^
^
^
^
^
^
^ ^
^
^
^
a^ a
v^ v^ at^0 ^
2 0 0
s^ s^
v t^ at ^
^
^
2 2 0
0 2 v^ v^
a^ s^ s ^
^ ^
0 0 (note)^
&^ : displacement & velocity when
s^ v^
t^
(2/2)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Kinematics of Particles
Rectilinear Motion VI
Rectilinear Motion
Graphical Interpretations (Time Response)
^ Velocity = Slope of a tangential line ^ Acceleration = Slope of a tangential line ^ (net displacement from
t1tot^
)=(area under
v-t curve)
^ Jerk = Slope of a tangential line ^ (net change in velocity b/w
t1and^
t2)=(area under^
a-t curve)
i)^ ds^ ,^ ii)
dv v^
a dt^
dt ^
^
(2/2)
Dynamics
P Kim (Chonbuk National University)
Undergraduate course, 2
nd^ year
Kinematics of Particles
Rectilinear Motion VII
Rectilinear Motion
Graphical Relations
iii)^ vdv^ ads^ ^ Net area under
a-s curve (Slope at A)
dv^
CB^
dv CB^ v^
a
ds^ v
ds
^ ^
^
^
(2/2)