A285832 Decimal expansion of the total area of a standard phugoid.

1, 6, 9, 0, 9, 7, 6, 6, 6, 3, 9, 6, 9, 0, 0, 1, 8, 3, 3, 7, 2, 1, 6, 4, 6, 9, 8, 2, 7, 8, 1, 1, 9, 6, 9, 6, 6, 2, 1, 4, 1, 6, 9, 5, 8, 4, 2, 0, 4, 5, 1, 7, 2, 7, 4, 7, 0, 5, 6, 5, 2, 4, 0, 9, 6, 5, 9, 4, 8, 0, 4, 9, 4, 2, 9, 8, 1, 8, 3, 4, 7, 9, 4, 3, 9, 3, 1, 0, 8, 8, 9, 6, 6, 2, 7, 7, 5, 2, 9, 4, 8, 3, 9, 7, 9

Offset

1,2

Comments

The curve crosses the x-axis at (4k-1)/4*Pi.

Links

Table of n, a(n) for n=1..105.

Mark Peters and Michael A. Konyak, The Engineering Analysis and Design of the Aircraft Dynamics Model For the FAA Target Generation Facility

Nicolas J. Schindeler, Phugoid Damping Control

Zachary S. Tseng, Mechanical Vibrations

Wikipedia, Phugoid

Formula

Sum_{n=0..inf} (-1)^n * Integral_{x=(4n-1)*Pi/4..(4n+3)*Pi/4} (cos(x) + sin(x))/e^x.

Example

1.690976663969001833721646982781196966214169584204517274705652409659480494298183...

Mathematica

Sum[(-1)^n*NIntegrate[ Exp[-x] (Cos[x] + Sin[x]), {x, (4n -1)Pi/4, (4n +3)Pi/4}, AccuracyGoal -> 128, PrecisionGoal -> 128, WorkingPrecision -> 156], {n, 0, 115}]
(* to view the curve *) Plot[Exp[-x] (Cos[x] + Sin[x]), {x, -3/4 Pi, 11/4 Pi}]

Crossrefs

Sequence in context: A298517 A199451 A135154 * A187798 A371321 A339802

Adjacent sequences: A285829 A285830 A285831 * A285833 A285834 A285835

Keyword

nonn,cons

Author

Robert G. Wilson v, Apr 27 2017

Status

approved