ME
–
210
Applied Mathematics for Mechanical Engineers
Prof. Dr. Faruk Arınç
Spring 2010
The tangent to a curve C at a point A on it is defined as the limiting position of the
straight line L through A and B, as B approaches A along the curve as illustrated
in the Figure.
Here,
it
is
assumed
that
the
curve
C
is
represented
by
a
continuously
differentiable (i.e., derivative exists and is continuous) vector function
, where
t is some parameter, the points A and B correspond to t and t +
Δt
. Then the
straight line L has the direction of the vector
Tangent and Arc Length of a Curve
)
t
(
r
)
t
(
r
)
t
t
(
r
r

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ME
–
210
Applied Mathematics for Mechanical Engineers
Prof. Dr. Faruk Arınç
Spring 2010
)
t
(
r
)
t
(
r
)
t
t
(
r
)
t
(
r
A
B
Tangent
L
O
x
y
z
C
)
t
(
T
Δs: Arc Length
from A to B
Tangent to a Curve
)
t
(
r
)
t
t
(
r
r