Numerical Solutions of the N-Body ProblemApproach your problem from the right It isn't that they can't see end and begin with the answers. the solution. Then one day, perhaps you will find It is that they can't see the the final question. problem. G.K. Chesterton. The Scandal The Hermit Clad in Crane Feathers in of Father Brown The Point of R. van Gulik's The Chinese Maze Murders. a Pin. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new brancheq. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisci fI plines as "experimental mathematics", "CFD , "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. |
Contents
Appendix PLI PROCEDURES | 13 |
THE GENERAL NBODY PROBLEM | 49 |
INDEX | 84 |
Copyright | |
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a₁ accuracy Algorithm applied arbitrary asymptotic expansion automatic step Butcher method C₁ C₂ center of mass coefficients components of velocity compute constants of motion denotes discrete mechanics method discretization method equations of motion exact solution explicit method fourth order frame of reference function GO TO LAB1 Gragg method gravitational constant Greenspan ij ij inertial frame initial value problem iteration process k)li k+1 k k+1 k+1 k+1 Lemma let us assume Let us note li li m₁ material points method of fourth multistep methods N-body problem number of bodies numerical methods obtain p+3N polynomial extrapolation problem of relative proof relative motion Richardson extrapolation Runge-Kutta method s=k or s=k+1 step size correction Table taking into account Theorem total discretization error two-body problem Vli characteristics constants xk+1 Xli Vli characteristics Yp+3N Σ Σ