General References

Graduate level

 * Heggie, D., and P. Hut. 2003. The gravitational million-body problem. A multidisciplinary approach to star cluster dynamics. Cambridge : Cambridge University Press.

Most pertinent to the physical target of the MICA endeavor. A substantial fraction of the book is devoted to the mathematical and computational techniques involved in numerical simulations. It covers from the 2-body problem up to star clusters.


 * Aarseth, S.J. 2003. Gravitational N-body simulations. Cambridge : Cambridge University Press.

A summa of knowledge by one of the pioneers and leaders in the field. Unfortunately it is very expensive, but a copy can certainly be found in the university libraries of astronomy or physics departments.


 * Binney, J., and S. Tremaine. 2008. Galactic dynamics. 2nd ed. Princeton, NJ : Princeton University Press.

The most comprehensive textbook on galactic dynamics. It covers from the 2-body problem to interacting galaxies, even touching on the branches of cosmology interesting for galaxies. The second edition has many sections about numerical techniques and simulations.


 * Valtonen, M., and H. Karttunen. 2006. The three-body problem. Cambridge : Cambridge University Press.

A very modern textbook on this unsolved problem still open for new research, though it is perhaps the oldest problem in Newtonian astrophysics. The text is well updated on recent discoveries, and contains much of the physics and mathematical techniques also used in N-body problems.


 * Bertin, G. 2000. Dynamics of galaxies. Cambridge : Cambridge University Press.

More physically than astronomically flavored. It deals with the same subject as Binney & Tremaine's Galactic dynamics, but with a somewhat different approach. It often works on the analogy between gravitationally interacting particles in a stellar system and electromagnetically interacting particles in a plasma.


 * Spitzer, L.Jr. 1987. Dynamical evolution of globular clusters. Princeton, NJ : Princeton University Press.

It was the standard reference for globular clusters, before the publication of Heggie & Hut's book. No longer published. Still interesting.


 * Murray, C.D., and S.F. Dermott. 1999. Solar system dynamics. Cambridge : Cambridge University Press.

A great book on the N-body problem in the Solar system.

On descriptive galactic astronomy

 * Binney, J., and M. Merrifield. 1998. Galactic astronomy. Princeton, NJ : Princeton University Press.

It is the companion book to Binney & Tremaine's Galactic dynamics. It gathers all the astronomical knowledge needed in applications of N-body to real galaxies.


 * Mihalas, D., and J. Binney. 1981. Galactic astronomy. Structure and kinematics. New York, NY : W.H: Freeman and Co.

It is the first edition of the previous entry ; it was the companion book to the first edition of Binney & Tremaine's Galactic dynamics. Though outdated and superseded by the new edition, it is a very inspired book, well written and yet full of interesting information.

Undergraduate level

 * Sparke, L.S., and J.S. Gallagher, III. 2007. Galaxies in the Universe. An introduction. 2nd ed. Cambridge : Cambridge University Press.

At the level of undergraduates majoring in physics, but not at all trivial. It gathers a lot of useful physics and astronomy, interesting even for researchers. It has pedagogical exercises throughout, and features a well annotated bibliography providing a wise guide through a vast astrophysical literature. This book is very clear and well-written, updated to the most recent discoveries. It does not require mathematical knowledge beyond derivatives and easy double integrals.

Elementary level

 * Jones, M.H., and R.J.A. Lambourne, eds. 2003. An introduction to galaxies and cosmology. Cambridge : The Open University and Cambridge University Press.

It is for the layman as to the level of mathematical knowledge required. Nonetheless, it is very interesting, since it is clearly written, contains the latest discoveries ( at the date of publication ), is well illustrated by images, figures, tables, insets. It simply explains all the physical and astronomical concepts that researchers deal with.


 * Celletti, A., and E. Perozzi. 2007. Celestial mechanics. The waltz of the planets. Berlin : Praxis Publishing Ltd.

An interesting book for the layman with chapters on the three-body problem, resonances, tidal friction, i.e. all the interesting stuff and most modern theories applied to the Solar system. No mathematical difficulties at all.

Review articles on the dynamics of star clusters

 * Elson, R., P. Hut, and S. Inagaki. 1987. Dynamical evolution of globular clusters. Ann. Rev. Astron. Astrophyis., 25 : 565-601.


 * Lightman, A.P., and S.L. Shapiro. 1978. The dynamical evolution of globular clusters. Reviews of Modern Physics, 2 : 437 - 481.

More references
We can find more references on the N-body problem at a webpage of the MODEST/Manybody consortium.

There is also a list of references in the Scholarpedia article on N-body simulations by M. Trenti and P. Hut.

Graduate level

 * Landau, L.D., and E.M. Lifshitz. 1976. Mechanics. Course of theoretical physics : volume 1. 3rd ed. Burlington, MA : Elsevier Science Ltd.

A real masterwork by Landau, a Nobel prize winner and one of the greatest physicists of the second third of last century, together with his coworker. Mechanics is built on the least action principle. Very elegant and terse. As David Goodstein of CalTech commented, it was written as if every word was to be chiseled on marble.


 * Arnold, V.I. 1989. Mathematical methods of classical mechanics. 2nd ed. New York, NY : Springer-Verlag.

A modern and authoritative book on Newtonian mechanics. It uses the most advanced mathematical views, but in a way wise and enlightening on the underlying physics and geometry, not with pedantry or perverse pleasure for hiding physical concepts behind difficult formalism.


 * Sussman, G.J., and J. Wisdom. 2000. Structure and interpretation of classical mechanics. Cambridge, MA : The MIT Press.

A textbook for the third millennium. Designed not around the few exactly integrable problems, but for the whole class of mechanical problems, now numerically solvable by digital computers. Thus it starts from the principles and grows around the equations that allow the greatest generality. Enthusiastically welcome by experts. Better reviewed by Piet Hut in Foundations of Physics, 32, 323-326, ( 2002 ). An online version of this book is available from the MIT Press. Also see the 2002 course on Classical Mechanics : a Computational Approach by the book's authors in the MIT Open CourseWare.


 * José, J.V., and E.J. Saletan. 1998. Classical dynamics : a contemporary approach. Cambridge : Cambridge University Press.

A fully modern textbook that devotes more than just a chapter to chaos and recent discoveries.

Undergraduate level

 * Shu, F.H. 1982. The physical Universe. An introduction to astronomy. Sausalito, CA : University Science Books.

A superb book on general astronomy. It covers from the basic physical laws to the emergence of life on Earth. Though outdated as to the recent astrophysical discoveries, it is surprisingly clear and deep. It explains astrophysical phenomena by using just concepts with almost no mathematics at all, so as to make readers understand the real physics behind them. It has a chapter on the laws of classical physics.


 * Karttunen, H, P. Kroeger, H. Oja, M. Poutanen, and K.J. Donner, eds. 2007. Fundamental astronomy. 5th ed. New York, NY : Springer-Verlag.

A modern and updated textbook on general astronomy. It has a chapter on celestial mechanics, clearly written, containing all the interesting information ( Newton's laws, equations of motion, orbits, 2-body problem, virial theorem ), with just undergraduate mathematics.

Graduate level

 * Arnold, V.I. 1973. Ordinary differential equations. Cambridge, MA : The MIT Press.

A modern book on the mathematics of dynamical systems.


 * Perko, L. 2001. Differential equations and dynamical systems. 3rd ed. New York, NY : Springer-Verlag.

One of the best books on the mathematics of chaotic dynamics. Mathematically flavored, but it does not require mathematical knowledge outside the usual background of physics ( or astronomy or engineering ) graduate students.

Undergraduate level

 * Strogatz, S.H. 1994. Nonlinear dynamics and chaos. With applications to physics, biology, chemistry, and engineering. Cambridge, MA : Perseus Books Publishing.

One of the best books on chaotic dynamics. Written by an author winner of many teaching prizes. Physically flavored.

References on computational techniques

 * Press, W.H., S.A. Teukolsky, W.T. Vetterling, and B.F. Flannery. 2007. Numerical recipes. The art of scientific computing. 3rd ed. Cambridge : Cambridge University Press.

One of the most used and cited books for numerical computations. The second edition was freely available on the web through a special arrangement between the Cornell University and the Cambridge UP. It seems that codes from the third edition are copyrighted. The second edition was really very very interesting since it provided the best algorithms for all kinds of problems normally encountered. It is written by researchers in astrophysics. Being encyclopaedic in coverage, it does not deal with proofs of methods, just with their use.


 * Acton, F.S. 1996. Real computing made real. Preventing errors in scientific and engineering calulations. Princeton, NJ : Princeton University Press.

A very interesting book on numerical techniques, focused on explaining the importance of wisdom and understanding in the application of algorithms taken from recipe books. Reissued by Dover Publications in a thrift edition.


 * Bender, C.M., and S.A. Orszag. 1978. Advanced mathematical methods for scientists and engineers. Asymptotic methods and perturbation theory. New York, NY : Springer-Verlag.

A very insightful book on the approximate solution of differential equations and more.


 * Abramowitz, M., and I.A. Stegun. 1964. Handbook of mathematical functions with formulas, graphs, and mathematical tables. National Bureau of Standards ; New York, NY : Dover Publications ( 1972 reissue ).

A must reference for numerical computations. Sooner or later anybody seriously doing numerical computing will need to look up something from it, at least.