本文選題：混沌-重力-方法:數(shù)值-天體力學(xué)-行星和衛(wèi)星:動力學(xué)演化和穩(wěn)定 + 核-殼時空�。� 參考：《南昌大學(xué)》2017年碩士論文

【摘要】：Pihajoki提出了一種適用于不可分離哈密頓系統(tǒng)的二階顯式相空間擴(kuò)充的的對稱蛙跳積分方法。在這個基礎(chǔ)上,我們在擴(kuò)充的相空間中如何組合這些變量的方法上提出了一些見解。數(shù)據(jù)測試表明,連續(xù)的置換坐標(biāo)和動量可以使類似的蛙跳算法得到更加準(zhǔn)確的計算結(jié)果和最佳的長時間穩(wěn)定性,我們也提出了一個新的方法用來構(gòu)建許多四階顯式相空間擴(kuò)充的類辛算法,每種算法都是由六個常用的不經(jīng)過任何排列的蛙跳算法構(gòu)成的。這種構(gòu)建模式由四部分組成:置換坐標(biāo),沒有置換的三個二階蛙跳格式的積分,置換動量,沒有置換的三個二階蛙跳格式的積分。同理,在擴(kuò)充的相空間中六階,八階,甚至更高階顯式類辛算法都是可以得到的。我們用一些常見的不可分離的哈密頓系統(tǒng)為例,就像有后牛頓項的無旋轉(zhuǎn)的致密雙星系統(tǒng)來證明我們提出的四階算法要優(yōu)于目前已知的算法,也包括了在Chin系統(tǒng)中的四階辛算法和四階顯式和隱式中點法混合的辛算法。當(dāng)給予適當(dāng)?shù)某跏贾禃r,我們可以發(fā)現(xiàn)顯式相空間擴(kuò)充的類辛算法更適合用于不可分離的哈密頓模型中,這些模型包括太陽系系統(tǒng)中常用的帶微小擾動的重力系統(tǒng)和具有后牛頓項的自旋的致密雙星系統(tǒng)。之后我們將之用于更加復(fù)雜的哈密頓系統(tǒng)中,并討論二階,四階,八階的性質(zhì),討論相對論核-殼系統(tǒng)的測地線方程的一些物理學(xué)性質(zhì)。最穩(wěn)定的圓形軌道的半徑在赤道平面只取決于四極矩。給定的扁圓的四極矩會導(dǎo)致兩個最穩(wěn)定的圓形軌道存在,它們的半徑大于史瓦西半徑。然而,一個扁長的四極矩只對應(yīng)一個最穩(wěn)定的圓軌道,其半徑小于史瓦西半徑。在一般的測地線軌道中,上述的四階顯式相空間空充的對稱算法能有效的運用到這個哈密頓系統(tǒng)中,盡管它們相對論中核與殼不能分離開來。借助這樣的積分方法,可以快速的計算這個軌道并且不會伴隨能量誤差的增長。這些核殼之間極矩對測地線方程的影響是由數(shù)值估計的。
[Abstract]:Pihajoki proposes a symmetric leapfrog integral method for second order explicit phase space expansion for inseparable Hamiltonian systems. On this basis, we put forward some ideas on how to combine these variables in the extended phase space. The data test shows that continuous permutation coordinates and momentum can make the similar leapfrog algorithm more accurate calculation results and the best long-term stability. We also propose a new method to construct many symplectic algorithms with fourth-order explicit phase space expansion. Each algorithm is composed of six commonly used leapfrog algorithms without any arrangement. The construction model consists of four parts: permutation coordinate, integration of three second-order leapfrog schemes without permutation, permutation momentum, and integration of three second-order leapfrog schemes without permutation. Similarly, explicit symplectic algorithms of order 6, order 8, and even higher order can be obtained in extended phase space. We take some common inseparability Hamiltonian systems as examples, such as dense binary systems with post-Newtonian terms that do not rotate to prove that our fourth order algorithm is superior to the current known algorithm. It also includes the fourth order symplectic algorithm in Chin system and the hybrid symplectic algorithm of four order explicit and implicit intermediate point method. When given a proper initial value, we can find that the symplectic algorithm with explicit phase space expansion is more suitable for the inseparability Hamiltonian model. These models include gravity systems with small perturbations commonly used in the solar system and dense binary systems with post-Newtonian spin. Then we apply it to more complex Hamiltonian systems and discuss the properties of second order, fourth order and eighth order, and discuss some physical properties of geodesic equations of relativistic core-shell systems. The radius of the most stable circular orbit in the equatorial plane depends only on the quadrupole moment. The quadrupole moment of a given flat circle results in the existence of two most stable circular orbits with a radius larger than that of Schwarzie. However, a flat and long quadrupole moment only corresponds to the most stable circular orbit and its radius is smaller than that of Schwarzie. In a general geodesic orbit, the above four order explicit phase space space-filled symmetry algorithm can be effectively applied to this Hamiltonian system, even though the core and shell can not be separated in their relativistic theory. With the help of this integral method, the orbit can be calculated quickly without increasing the energy error. The effect of polar moments between core-shell on geodesic equations is estimated numerically.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：P13

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本文編號：2016744