A non-dimensional model of a glider flying to minimise flight-time in the absence of lift and drag is COSY = u' u = - - sin y " U {' = u cosy, n' = usin y where is the flight-path angle, u is the non-dimensional velocity, § is the non-dimensional range, and ʼn is the non-dimensional altitude and ' (prime) denotes differentiation with respect to 7, the non-dimensional time. The glider travels from § = 0,ŋ = 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. Find differential equations for dε/dy and dn/dy. and the general solutions of the differential equations
A non-dimensional model of a glider flying to minimise flight-time in the absence of lift and drag is COSY = u' u = - - sin y " U {' = u cosy, n' = usin y where is the flight-path angle, u is the non-dimensional velocity, § is the non-dimensional range, and ʼn is the non-dimensional altitude and ' (prime) denotes differentiation with respect to 7, the non-dimensional time. The glider travels from § = 0,ŋ = 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. Find differential equations for dε/dy and dn/dy. and the general solutions of the differential equations
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
COSY
u' = = sin y
น
ૐ = u cosy, n' = usin y
where is the flight-path angle, u is the non-dimensional velocity, & is the
non-dimensional range, and n is the non-dimensional altitude and' (prime)
denotes differentiation with respect to 7, the non-dimensional time.
=
The glider travels from § = 0,ŋ = 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.
Find differential equations for dε/dy and dn/dy.
and the general solutions of the differential equations
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