The curvature of a circle is defined as 1/r, where r is the radius of the circle. Therefore, smaller circles have higher curvature and larger circles have lower curvature. The curvature of a straight line is 0, since straight lines are considered "flat" with no curvature.
This presentation explains about the introduction of Polar Plot, advantages and disadvantages of polar plot and also steps to draw polar plot. and also explains about how to draw polar plot with an examples. It also explains how to draw polar plot with numerous examples and stability analysis by using polar plot.
This presentation explains about the introduction of Nyquist Stability criterion. It clearly shows advantages and disadvantages of Nyquist Stability criterion and also explains importance of Nyquist Stability criterion and steps required to sketch the Nyquist plot. It explains about the steps required to sketch Nyquist plot clearly. It also explains about sketching Nyquist plot and determines the stability by using Nyquist Stability criterion with an example.
What is Fourier Transform
Spatial to Frequency Domain
Fourier Transform
Forward Fourier and Inverse Fourier transforms
Properties of Fourier Transforms
Fourier Transformation in Image processing
Introduction, classification of curves, Elements of a simple circular, designation of curve, methods of setting out a simple circular curve, elements of a compound and reverse curves, transition curve, types of transition curves, combined curve, types of vertical curves
This presentation explains about the introduction of Polar Plot, advantages and disadvantages of polar plot and also steps to draw polar plot. and also explains about how to draw polar plot with an examples. It also explains how to draw polar plot with numerous examples and stability analysis by using polar plot.
This presentation explains about the introduction of Nyquist Stability criterion. It clearly shows advantages and disadvantages of Nyquist Stability criterion and also explains importance of Nyquist Stability criterion and steps required to sketch the Nyquist plot. It explains about the steps required to sketch Nyquist plot clearly. It also explains about sketching Nyquist plot and determines the stability by using Nyquist Stability criterion with an example.
What is Fourier Transform
Spatial to Frequency Domain
Fourier Transform
Forward Fourier and Inverse Fourier transforms
Properties of Fourier Transforms
Fourier Transformation in Image processing
Introduction, classification of curves, Elements of a simple circular, designation of curve, methods of setting out a simple circular curve, elements of a compound and reverse curves, transition curve, types of transition curves, combined curve, types of vertical curves
Angles, Triangles of Trigonometry. Pre - Calculusjohnnavarro197
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This presentation will help learners to grasp and understand trigonometry concepts such as angles, triangles. It encompasses basic fundamental topics of trigonometry.
1. A circle of radius r has a curvature of size 1/r.
Therefore, small circles have large curvature
and large circles have small curvature. The
curvature of a line is 0. In general, an object
with zero curvature is "flat."
2. Curvature
The act of curving
The state of being curved.
๏ฑ The ratio of the change in the angle of a
tangent that moves along curve from
point to point
๏ฑThe limit of the ratio of the change in the
angle of a tangent as arc length
approaches zero
๏ฑThe reciprocal of the radius of a circle.
3. Let C:๐ = ๐(๐ ) be a space curve and P be a point on it,
then curvature at ๐ is defined as rate of rotation of
tangent (change in the direction of tangent) at ๐. Its
magnitude is denoted by ๐ (kappa) and defined by
๐ฟ๐ ๐๐
๐ = ๐๐๐ ๐ฟ๐ = ๐๐
๐ฟ๐ โ0
Where ๐ฟ๐ is the angle between tangents at points ๐ and
๐ on the curve along arc length ๐ฟ๐ .
tangent
๐ฟ๐
tangent
C:๐ = ๐(๐ )
4. More precisely, curvature is
โขScalar measure of bending nature of the curve
โขDegree of curving in a line
โขChange in the direction of tangent line
โขArc rate of rotation of tangent line from point to point
โขChange in principal normal along tangent direction
5. Curvature measures the rate at which a space curve ๐(t) changes direction.
The direction of curve is given by the unit tangent vector
๐(๐)
๐(๐) =
๐(๐)
which has length 1 and is tangent to ๐(t).
The picture below shows the unit tangent vector ๐ to the curve ๐(t) =(2cos(t), sin(t), 0)
at several points.
Obviously,
if ๐(t) is a straight line, the curvature is 0.
Otherwise the curvature is non-zero.
To be precise, curvature is defined to be the
magnitude of the rate of change of the unit
tangent vector with respect to arc length:
๐ ๐
๐ ๐
๐=
๐ ๐
๐ ๐
6. Note
1. Straight line has zero curvature
2. A circle has constant curvature
3. A circular helix has constant curvature
4. The curvature of small circle is large and vice versa
1
5. The radius of curvature is denoted by ๐, i.e ๐ = ๐