HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES
HES2310 - Dynamics-1
Jamal Naser
Senior Lecturer
EN216
Ext: 8655
Swinburne University
NB: These lecture notes are prepared from “Engineering
Mechanics-
Dynamics” (the book by J.L. Merium & L.G.
Kraige). These notes will help the students to follow lectures in
the class.
Students should read the book. Students should not
depend on these lecture notes only.
HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES
Location & path of a particle in space
•
Location can be defined in
–
rectangular cordinates by x, y, z
–
cylindrical coordunates by r,
θ
, z
–
spherical coordinates by R,
θ,
φ
•
Path in space can be
– constrained
•
guided in a defined path
– unconstrained
•
no defined path
HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES
Rectilinear motion
•
The dislacement of the particle in time
∆
t is
∆
s
– hence the velocity is v=lim
(
∆
t
0)
∆
s/
∆
t
s
∆
s
t=0
t=t
t=t+
∆
t
-s
+s
a
dv
dt
v
or
a
d
s
dt
s
=
=
=
=
/
D
/
DD
( )
2
2
2
v
ds
dt
s
=
=
/
D
( )
1
v
ds
a
dv
or
vdv
ads
or
sds
sds
/
/
D D
DD
( )
=
=
=
3
HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES
Graphical relationships between s, v, a & t
Tangent to curve in Fig(a) gives
Velocity= v = ds/dt
velocity at all ponnts determined
and plotted in Fig (b)
Tangent to curve in Fig(b) gives
Acceleration= a =dv/dt
Area under the v-t curve is:
v dt = ds , on integration :
ds
vdt
s
s
s
s
v
v
1
2
1
2
2
1
∫
∫
=
=
−
HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES
accelerations at all ponnts
determined and plotted in Fig (c)
Shaded area under the a-t curve is:
adt = dv , on integration :
Change in velocity
dv
adt
v
v
v
v
t
t
1
2
1
2
2
1
∫
∫
=
=
−
These graphical representations are important for:
1. Visualizing the relationship between s, v, a & t
2. Approximating results by graphical integration or
Differencation when mathematical functions & relationships are
not available
HES 2310 LECTURE NOTES DEVELOPED BY DR JAMAL NASER FOR HIS LECTURES
Acceleration Vs distance plot gives
ads = vdv = d(v
2
/2)
Integrating Net Area under a-s curve
vdv
ads
v
v
v
v
s
s
1
2
1
2
1
2
2
2
1
2
∫
∫
=
=
−
(
)
From the similar triangles in Fig.(b)
CB/v = dv/ds
CB=vdv/ds = a

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