This paper will present the results and analyses of a simulation to send a satellite from the Earth to Mars. We use Python to simulate the orbit of the rocket. Our goal is to find the least energy-cost trajectory, wit...This paper will present the results and analyses of a simulation to send a satellite from the Earth to Mars. We use Python to simulate the orbit of the rocket. Our goal is to find the least energy-cost trajectory, with the least initial velocity. We find the date which allows the satellite to go from the Earth to Mars in the shortest distance based on a Hohmann transfer orbit considering the gravity of the Sun, Earth, and Mars.展开更多
2004年3月8日,Bill Venners在加州的圣尼威尔采访了Luke Hohmann。他们一起讨论了软件架构师的社会角色,如何专注于产品不同版本的意义,以及行业知识的重要性。 Luke Hohmann是一位管理咨询顾问,他帮助客户消除在业务和技术之间存在的...2004年3月8日,Bill Venners在加州的圣尼威尔采访了Luke Hohmann。他们一起讨论了软件架构师的社会角色,如何专注于产品不同版本的意义,以及行业知识的重要性。 Luke Hohmann是一位管理咨询顾问,他帮助客户消除在业务和技术之间存在的隔膜。Luke曾经担当过多种不同的角色,包括:开发、营销、专家服务、销售、客户服务,商务发展。Hohmann目前把工作重心放在企业级软件系统上。他是《软件专家的历程:软件开发的社会学》(Prentice-Hall,1997)一书的作者,这本书将认知心理学和组织行为学揉合在一起,形成一个在软件开发过程中对人员进行管理的模型。他还是《超越软件架构:建立和维持致胜的解决方案》(Addison-Wesley,2003)一书的作者,在这本书里,探讨了在商业环境中软件架构的作用。展开更多
Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constrai...Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constraint. By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove the global minimum of the Hohmann transfer. Two sets of feasible solutions are found: one corresponding to the Hohmann transfer is the global minimum and the other is a local minimum. We next formulate the Hohmann transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible solutions are also found by numerical examples. Via static and dynamic constrained optimizations, the solution to the Hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear programming.展开更多
The optimizing total velocity increment Δv needed for orbital maneuver between two elliptic orbits with plane change is investigated. Two-impulse orbital transfer is used based on a changing of transfer velo...The optimizing total velocity increment Δv needed for orbital maneuver between two elliptic orbits with plane change is investigated. Two-impulse orbital transfer is used based on a changing of transfer velocities concept due to the changing in the energy. The transferring has been made between two elliptic orbits having a common centre of attraction with changing in their planes in standard Hohmann transfer with the terminal orbit which is elliptic orbit and not circular. We develop a treatment based on the elements of elliptic orbits a1,e1, a2,e2, and?aT,eT of the initial orbit, final orbit and transferred orbit respectively. The first impulse Δv1 at the perigee induces a rotation of the orbital plane by ?which will be minimized. The second impulse Δv2 at apogee is induced an angle ?to product the final elliptic orbit. The total plane change required . We calculate the total impulse Δv and minimize by optimizing angle of plane’s variation . We obtain a polynomial equation of six degrees on the two transfer angles between neither two elliptic orbits ?and . The solution obtained numerically, using programming code of MATHEMATICA V10, with no condition on the eccentricity or the semi-major axis of the initial, transformed, and the final orbits. We find that there are constrains on the transfer angles and α. For αit must be between 40°and 160°, and there is no solution if αis less than 40°and bigger than 160°and ?takes the values less than 40°. The minimum total velocity increments obtained at the value of ?less than 25°and& alpha;equal to 160°. This is an interesting result in orbital transfer problem in which the change of orbital plane is necessary for the transferring.展开更多
文摘This paper will present the results and analyses of a simulation to send a satellite from the Earth to Mars. We use Python to simulate the orbit of the rocket. Our goal is to find the least energy-cost trajectory, with the least initial velocity. We find the date which allows the satellite to go from the Earth to Mars in the shortest distance based on a Hohmann transfer orbit considering the gravity of the Sun, Earth, and Mars.
文摘2004年3月8日,Bill Venners在加州的圣尼威尔采访了Luke Hohmann。他们一起讨论了软件架构师的社会角色,如何专注于产品不同版本的意义,以及行业知识的重要性。 Luke Hohmann是一位管理咨询顾问,他帮助客户消除在业务和技术之间存在的隔膜。Luke曾经担当过多种不同的角色,包括:开发、营销、专家服务、销售、客户服务,商务发展。Hohmann目前把工作重心放在企业级软件系统上。他是《软件专家的历程:软件开发的社会学》(Prentice-Hall,1997)一书的作者,这本书将认知心理学和组织行为学揉合在一起,形成一个在软件开发过程中对人员进行管理的模型。他还是《超越软件架构:建立和维持致胜的解决方案》(Addison-Wesley,2003)一书的作者,在这本书里,探讨了在商业环境中软件架构的作用。
基金supported by the National Natural Science Foundation of China(No.61374084)
文摘Inspired by the geometric method proposed by Jean-Pierre MAREC, we first consider the Hohmann transfer problem between two coplanar circular orbits as a static nonlinear programming problem with an inequality constraint. By the Kuhn-Tucker theorem and a second-order sufficient condition for minima, we analytically prove the global minimum of the Hohmann transfer. Two sets of feasible solutions are found: one corresponding to the Hohmann transfer is the global minimum and the other is a local minimum. We next formulate the Hohmann transfer problem as boundary value problems, which are solved by the calculus of variations. The two sets of feasible solutions are also found by numerical examples. Via static and dynamic constrained optimizations, the solution to the Hohmann transfer problem is re-discovered, and its global minimum is analytically verified using nonlinear programming.
文摘The optimizing total velocity increment Δv needed for orbital maneuver between two elliptic orbits with plane change is investigated. Two-impulse orbital transfer is used based on a changing of transfer velocities concept due to the changing in the energy. The transferring has been made between two elliptic orbits having a common centre of attraction with changing in their planes in standard Hohmann transfer with the terminal orbit which is elliptic orbit and not circular. We develop a treatment based on the elements of elliptic orbits a1,e1, a2,e2, and?aT,eT of the initial orbit, final orbit and transferred orbit respectively. The first impulse Δv1 at the perigee induces a rotation of the orbital plane by ?which will be minimized. The second impulse Δv2 at apogee is induced an angle ?to product the final elliptic orbit. The total plane change required . We calculate the total impulse Δv and minimize by optimizing angle of plane’s variation . We obtain a polynomial equation of six degrees on the two transfer angles between neither two elliptic orbits ?and . The solution obtained numerically, using programming code of MATHEMATICA V10, with no condition on the eccentricity or the semi-major axis of the initial, transformed, and the final orbits. We find that there are constrains on the transfer angles and α. For αit must be between 40°and 160°, and there is no solution if αis less than 40°and bigger than 160°and ?takes the values less than 40°. The minimum total velocity increments obtained at the value of ?less than 25°and& alpha;equal to 160°. This is an interesting result in orbital transfer problem in which the change of orbital plane is necessary for the transferring.
