Journal ArticleDOI
Numerical Integration of Ordinary Differential Equations
TLDR
In this article, the integration of Ordinary Differential Equations (ODE) has been studied in the context of algebraic geometry, and it has been shown that it is possible to integrate ODEAbstract:
(1926). Numerical Integration of Ordinary Differential Equations. The American Mathematical Monthly: Vol. 33, No. 9, pp. 455-460.read more
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Artillerymen and mathematicians: Forest Ray Moulton and changes in American exterior ballistics, 1885–1934
TL;DR: The authors focused on the efforts of Forest Ray Moulton and details how he dealt with various aspects of a single problem: differential variations in the ballistic trajectory due to known factors. But their focus was not on the dynamics of the trajectories.
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On Nordsieck's method for the numerical solution of ordinary differential equations
Abstract: The connection between the class of methods suggested by Nordsieck and the class of linear multi-step methods is examined. It is shown that the starting procedure suggested by Nordsieck is specially suited to the Adams method.
Journal ArticleDOI
A Modification of Nordsieck's Method Using an ``Off-Step'' Point
J. J. Kohfeld,G. T. Thompson +1 more
TL;DR: The method in the present paper is equivalent, for uniform step size, to one of these very accurate correctors but is in the form of Nordsieck, and the strengths and weaknesses of the method are discussed.
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Mechanistic details of energy transfer and soft landing in ala2-H+ collisions with a F-SAM surface
TL;DR: The ala2-H(+) + F-SAM simulations are compared with the penetration and trapping dynamics found in previous simulations of projectile + organic surface collisions and find the collisional energy transfers are overall insensitive to the trajectory type.
Journal ArticleDOI
Model Formulation Over Lie Groups and Numerical Methods to Simulate the Motion of Gyrostats and Quadrotors
TL;DR: In this paper, the Lagrange-d'Alembert principle is expressed through a generalized Euler-Poincare form of the system equation on a Lie group and applied to a gyrostat satellite and a quadcopter drone.