مسئله (n) جسم

در فیزیک، مسئله (n) جسم (انگلیسی: N-body problem) مشکل پیش‌بینی حرکت‌های فردی گروهی از اجرام آسمانی است که با یکدیگر تعامل گرانشی دارند. تمایل به درک حرکت خورشید، ماه، سیاره‌ها و ستارگان مرئی آسمان دیدن هستند در قرن ۲۰، عامل رسیدن به درک پویایی سیستم‌های ستاره‌ای خوشه‌ای کروی به یک مسئله مهم (n) جسم تبدیل شد. مسئله (n) جسم در نسبیت عام به دلیل عوامل اضافی مانند اعوجاج‌های زمان و مکان به‌طور قابل توجهی مشکل‌تر است.

مسئلهٔ فیزیکی کلاسیک را می‌توان به‌صورت غیررسمی به شرح زیر بیان کرد:

با توجه به خصوصیات مداری شبه ثابت (موقعیت لحظه‌ای، سرعت و زمان) از یک گروه از اجرام آسمانی، نیروهای تعاملی آنها را می‌توان پیش‌بینی کرد. و در نتیجه، حرکت مداری واقعی آنها را برای همه زمان‌های آینده پیش‌بینی کرد.

مسئله دو جسم به‌طور کامل حل شده‌است و در زیر بحث می‌شود، و همچنین مشکل مشهور محدودیت در سه جسم.

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منابع

↑ Leimanis and Minorsky: Our interest is with Leimanis, who first discusses some history about the $n$ -body problem, especially Ms. Kovalevskaya's 1868–1888 twenty-year complex-variables approach, failure; Section 1: "The Dynamics of Rigid Bodies and Mathematical Exterior Ballistics" (Chapter 1, "The motion of a rigid body about a fixed point (Euler and Poisson equations)"; Chapter 2, "Mathematical Exterior Ballistics"), good precursor background to the $n$ -body problem; Section 2: "Celestial Mechanics" (Chapter 1, "The Uniformization of the Three-body Problem (Restricted Three-body Problem)"; Chapter 2, "Capture in the Three-Body Problem"; Chapter 3, "Generalized $n$ -body Problem").
↑ See references cited for Heggie and Hut.
↑ Quasi-steady loads refers to the instantaneous inertial loads generated by instantaneous angular velocities and accelerations, as well as translational accelerations (9 variables). It is as though one took a photograph, which also recorded the instantaneous position and properties of motion. In contrast, a steady-state condition refers to a system's state being invariant to time; otherwise, the first derivatives and all higher derivatives are zero.
↑ R. M. Rosenberg states the $n$ -body problem similarly (see References): "Each particle in a system of a finite number of particles is subjected to a Newtonian gravitational attraction from all the other particles, and to no other forces. If the initial state of the system is given, how will the particles move?" Rosenberg failed to realize, like everyone else, that it is necessary to determine the forces first before the motions can be determined.
↑ A general, classical solution in terms of first integrals is known to be impossible. An exact theoretical solution for arbitrary $n$ can be approximated via Taylor series, but in practice such an infinite series must be truncated, giving at best only an approximate solution; and an approach now obsolete. In addition, the $n$ -body problem may be solved using numerical integration, but these, too, are approximate solutions; and again obsolete. See Sverre J. Aarseth's book Gravitational $n$ -Body Simulations listed in the References.

[Leimanis_and_Minorsky-1] Leimanis and Minorsky: Our interest is with Leimanis, who first discusses some history about the $n$ -body problem, especially Ms. Kovalevskaya's 1868–1888 twenty-year complex-variables approach, failure; Section 1: "The Dynamics of Rigid Bodies and Mathematical Exterior Ballistics" (Chapter 1, "The motion of a rigid body about a fixed point (Euler and Poisson equations)"; Chapter 2, "Mathematical Exterior Ballistics"), good precursor background to the $n$ -body problem; Section 2: "Celestial Mechanics" (Chapter 1, "The Uniformization of the Three-body Problem (Restricted Three-body Problem)"; Chapter 2, "Capture in the Three-Body Problem"; Chapter 3, "Generalized $n$ -body Problem").

[Heggie_and_Hut-2] See references cited for Heggie and Hut.

[3] Quasi-steady loads refers to the instantaneous inertial loads generated by instantaneous angular velocities and accelerations, as well as translational accelerations (9 variables). It is as though one took a photograph, which also recorded the instantaneous position and properties of motion. In contrast, a steady-state condition refers to a system's state being invariant to time; otherwise, the first derivatives and all higher derivatives are zero.

[4] R. M. Rosenberg states the $n$ -body problem similarly (see References): "Each particle in a system of a finite number of particles is subjected to a Newtonian gravitational attraction from all the other particles, and to no other forces. If the initial state of the system is given, how will the particles move?" Rosenberg failed to realize, like everyone else, that it is necessary to determine the forces first before the motions can be determined.

[5] A general, classical solution in terms of first integrals is known to be impossible. An exact theoretical solution for arbitrary $n$ can be approximated via Taylor series, but in practice such an infinite series must be truncated, giving at best only an approximate solution; and an approach now obsolete. In addition, the $n$ -body problem may be solved using numerical integration, but these, too, are approximate solutions; and again obsolete. See Sverre J. Aarseth's book Gravitational $n$ -Body Simulations listed in the References.