This textbook provides details of the derivation of Lagrange's
planetary equations and of the closely related Gauss's variational
equations, thereby covering a sorely needed topic in existing
literature. Analytical solutions can help verify the results of
numerical work, giving one confidence that his or her analysis is
correct. The authors-all experienced experts in astrodynamics and
space missions-take on the massive derivation problem step by step
in order to help readers identify and understand possible
analytical solutions in their own endeavors. The stages are
elementary yet rigorous; suggested student research project topics
are provided. After deriving the variational equations, the authors
apply them to many interesting problems, including the Earth-Moon
system, the effect of an oblate planet, the perturbation of
Mercury's orbit due to General Relativity, and the perturbation due
to atmospheric drag. Along the way, they introduce several useful
techniques such as averaging, Poincare's method of small
parameters, and variation of parameters. In the end, this textbook
will help students, practicing engineers, and professionals across
the fields of astrodynamics, astronomy, dynamics, physics,
planetary science, spacecraft missions, and others. "An extensive,
detailed, yet still easy-to-follow presentation of the field of
orbital perturbations." - Prof. Hanspeter Schaub, Smead Aerospace
Engineering Sciences Department, University of Colorado, Boulder
"This book, based on decades of teaching experience, is an
invaluable resource for aerospace engineering students and
practitioners alike who need an in-depth understanding of the
equations they use." - Dr. Jean Albert Kechichian, The Aerospace
Corporation, Retired "Today we look at perturbations through the
lens of the modern computer. But knowing the why and the how is
equally important. In this well organized and thorough compendium
of equations and derivations, the authors bring some of the
relevant gems from the past back into the contemporary literature."
- Dr. David A Vallado, Senior Research Astrodynamicist, COMSPOC
"The book presentation is with the thoroughness that one always
sees with these authors. Their theoretical development is followed
with a set of Earth orbiting and Solar System examples
demonstrating the application of Lagrange's planetary equations for
systems with both conservative and nonconservative forces, some of
which are not seen in orbital mechanics books." - Prof. Kyle T.
Alfriend, University Distinguished Professor, Texas A&M
University
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