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Realistic Simulations of Non-Linear Acceleration of the Rocket in the Air
American Journal of Physics and Applications
Volume 6, Issue 5, September 2018, Pages: 128-132
Received: Oct. 15, 2018; Accepted: Oct. 31, 2018; Published: Nov. 29, 2018
Author
Haoyuan Xiong, Beijing Haidian Foreign Language Shiyan School, Beijing, China
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Abstract
The motion of the object in the medium has always been a hot research topic, and it is closely connected with many applications in our life. The acceleration of the object with multiple forces becomes very complicated, especially when these forces depend on the motion of the object. The exact formula for the object motion is a differential-integral equation and is very difficult to be solved analytically. One example of this kind of motions is the rocket launch. With sufficient thrust, the rocket can obtain an acceleration large enough to escape from the gravity of the earth. With the increasing height, the gravity from the earth becomes smaller, which affects the net acceleration of the rocket. Meanwhile, the air resistance becomes more and more important when the velocity of the rocket increases. It even plays the main role in the middle stage of the launch. Also, as the air resistance depends on both the velocity of the rocket and the air density (there is no air resistance in vacuum), the air resistance will decrease when the air density becomes small enough at the large height. In this article, a model that includes all of the factors mentioned above is established, and how these forces change the velocity of the rocket is analyzed. Two scenarios, one with air resistance and one without, are described. The velocity of the rocket in each scenario is represented by graphs, which are compared. With justification, the Taylor series is used to solve the differential-integral equation, and it is found that the fuel thrust and the gravity become important in the rocket launch at the beginning stage. In the middle stage, the air resistance begins to have a significant effect and reduces the acceleration of the rocket. In the final stage, there is virtually no gravity or air resistance, and only the fuel thrust contributes to the acceleration of the rocket.
Keywords
Non-linear Acceleration, Taylor Expansion, Rocket Launch, Air Resistance, Gravity
Haoyuan Xiong, Realistic Simulations of Non-Linear Acceleration of the Rocket in the Air, American Journal of Physics and Applications. Vol. 6, No. 5, 2018, pp. 128-132. doi: 10.11648/j.ajpa.20180605.13
References
[1]
Hawren Fang Yousef Saad, Numereical linar algebra with applications, Volume16, Issue3, March 2009, Pages 197-221.
[2]
Le Cun, Yann. Deep learning [J]. NATURE, 2015, 521 (7553): 436-444.
[3]
Tariyal, Snigdha. Deep Dictionary Learning [J]. IEEE ACCESS, 2016, 4: 10096-10109.
[4]
Gerald James Holton and Stephen G. Brush (2001). Physics, the human adventure: from Copernicus to Einstein and beyond (3rd ed.).
[5]
Mnih, Volodymyr. Human-level control through deep reinforcement learning [J]. NATURE, 2015, 518(7540): 529-553.
[6]
Li, He. Learning IoT in Edge: Deep Learning for the Internet of Things with Edge Computing [J]. IEEE NETWORK, 2018, 32: 96-101
[7]
Hirt, C.; Claessens, S.; Fecher, T.; Kuhn, M.; Pail, R.; Rexer, M. (2013). "New ultrahigh-resolution picture of Earth's gravity field". Geophysical Research Letters. 40 (16): 4279–4283.
[8]
Yao, Shuochao. Deep Learning for the Internet of Things [J]. COMPUTER, 2018, 51(5): 32-41.
[9]
Qiao, Junfei. An adaptive deep Q-learning strategy for handwritten digit recognition [J]. NEURAL NETWORKS, 2018, 107: 61-71.
[10]
"NASA- Four forces on a model rocket". Grc. nasa. gov. 2000-09-19. Archived from the original on 2012-11-29. Retrieved 2012-12-10.
[11]
Damien Scieur, Alexandre D’Aspremont, Francis Bach. Nonlinear Acceleration of Stochastic Algorithms. 2017.
[12]
L. G. C. E. Pugh, J Physiol. 1971 Mar; 213(2): 255–276.
[13]
Robin Smith, Graham Peacock, Journal of Evaluation & Research in Education Volume 6, 1992 - Issue 2-3: Primary Science.
[14]
Ken Takahashi and D. Thompson, American Journal of Physics 67, 709 (1999);
[15]
Tomer Urca, Gal Ribak, Journal of Experimental Biology 2018: jeb.177600 doi: 10.1242/jeb.177600.
[16]
Allen T. Chwang and K. H. Wang, J. Fluids Eng 106(2), 233-240 (Jun 01, 1984).
[17]
Dapeng Zhu, Shock and Vibration Volume 2018, Article ID 7513971, 8 pages.
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