A non-dimensional model of a glider flying to minimise flight-time in the absence of lift and drag is COS Y ŕ = u' = - sin y ' ย §' = ucosy, n' = usin y where is the flight-path angle, u is the non-dimensional velocity, & is the non-dimensional range, and 7 is the non-dimensional altitude and' (prime) denotes differentiation with respect to 7, the non-dimensional time. The glider travels from § = 0,7 = ho to § = L,n = h₁, where ho > h1 > 0, and, at the start of the motion, the glider is pointing vertically downwards so that y = −π/2. u = ccosy for some constant c +0 dy/dT = 1/c. Show that the flight-path is given by a cycloid. How is the constant c determined? ho - (let x = {, y = họ − ŋ and 0 = π +2y.)
A non-dimensional model of a glider flying to minimise flight-time in the absence of lift and drag is COS Y ŕ = u' = - sin y ' ย §' = ucosy, n' = usin y where is the flight-path angle, u is the non-dimensional velocity, & is the non-dimensional range, and 7 is the non-dimensional altitude and' (prime) denotes differentiation with respect to 7, the non-dimensional time. The glider travels from § = 0,7 = ho to § = L,n = h₁, where ho > h1 > 0, and, at the start of the motion, the glider is pointing vertically downwards so that y = −π/2. u = ccosy for some constant c +0 dy/dT = 1/c. Show that the flight-path is given by a cycloid. How is the constant c determined? ho - (let x = {, y = họ − ŋ and 0 = π +2y.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A non-dimensional model of a glider flying to minimise flight-time in the
absence of lift and drag is
COS Y
ŕ
=
u' = - sin y
'
ย
§' = ucosy, n' = usin y
where is the flight-path angle, u is the non-dimensional velocity, & is the
non-dimensional range, and 7 is the non-dimensional altitude and' (prime)
denotes differentiation with respect to 7, the non-dimensional time.
The glider travels from § = 0,7 = ho to § = L,n = h₁, where ho > h1 > 0,
and, at the start of the motion, the glider is pointing vertically downwards so
that y = −π/2.
u = ccosy for some constant c +0
dy/dT = 1/c.
Transcribed Image Text:Show that the flight-path is given by a cycloid.
How is the constant c determined?
ho
-
(let x = {, y = họ − ŋ and 0 = π +2y.)
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