9.2.3 (A spherical trapping region) Show that all trajectories eventually enter and remain inside a large sphere S of the form x² + y² + (z-r-0)² = C, for Csuf- ficiently large. (Hint: Show that x² + y² + (z-r-o) decreases along trajectories for all (x,y,z) outside a certain fixed ellipsoid. Then pick Clarge enough so that the sphere S encloses this ellipsoid.)
9.2.3 (A spherical trapping region) Show that all trajectories eventually enter and remain inside a large sphere S of the form x² + y² + (z-r-0)² = C, for Csuf- ficiently large. (Hint: Show that x² + y² + (z-r-o) decreases along trajectories for all (x,y,z) outside a certain fixed ellipsoid. Then pick Clarge enough so that the sphere S encloses this ellipsoid.)
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:9.2.3 (A spherical trapping region) Show that all trajectories eventually enter
and remain inside a large sphere S of the form x² + y² + (z-r-o)² = C, for Csuf-
ficiently large. (Hint: Show that x² + y² + (z-r-o) decreases along trajectories
for all (x,y,z) outside a certain fixed ellipsoid. Then pick Clarge enough so that the
sphere S'encloses this ellipsoid.)
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