Numerical Differentiation - Numerical Methods in Engineering with MATLAB - page 198

=

The radar stations A and B ,separatedbythe distance a 500 m,track the plane

C by recording the angles α and β atone-second intervals. If three successive

readings are

t (s) 9 10 11

80 ◦ 06 ◦ 34 ◦ α 54 . 54 . 53 .

59 ◦ 59 ◦ 62 ◦

β 65 . 64 . 63 .

γ =

calculate the speed v of the plane and the climb angle at t 10s. The coordi-

nates of the planecan be shown to be

tan β tan α tan β

x = a y = a

tan β − tan α tan β − tan α

14.

20

D

β

C

Dimensions
in mm

190

α

A

θ

B

Geometric analysisofthelinkage shown resultedinthe following table relating
the angles θ and β :

θ (deg) 0 30 60 90 120 150

β (deg) 59 . 96 56 . 42 44 . 10 25 . 72 − 0 . 27 − 34 . 29

Assuming that member AB of the linkage rotates with the constant angular ve-
locity d

θ/ dt = 1rad/s, compute d β/ dt in rad/s at the tabulatedvalues of θ . Use

cubicspline interpolation.

MATLAB Functions

d = diff(y) returns the differences d(i) = y(i+1) - y(i) . Note that

length(d) = length(y) - 1 .