Approximations of Interplanetary Trajectories by Chebyshev Series

Nacozy, P. E.; Feagin, T.

doi:10.2514/3.50087

Cited by 5 publications

(2 citation statements)

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“…(3) when a unit change in some component of either x(0) or y has occurred. A convenient and well-performing expression (2) was found to be <MT) = i (k = 1) = T(l-T)7i_ 2 (2T-! T k (s) = cos (k arc cos s), in terms of Tchebyshev polynomials.…”

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confidence: 98%

“…l It has found applications in spaceflight trajectory optimization. 2 It is shown in this paper how the method can be adapted to the computation of trajectories within a combined design/performance optimization program for multistage launch vehicles. The parameters of the collocation expansion are adjusted in a single loop, together with the primary control variables of the problem, to satisfy the conditions of a constrained optimum.…”

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High-speed Computation of Ascent Trajectories within Iterative Loops Using Collocation Methods

Hempel¹

1974

AIAA Journal

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ThemeT HE collocation method is a convenient tool for the numerical solution of differential equations. l It has found applications in spaceflight trajectory optimization. 2 It is shown in this paper how the method can be adapted to the computation of trajectories within a combined design/performance optimization program for multistage launch vehicles. The parameters of the collocation expansion are adjusted in a single loop, together with the primary control variables of the problem, to satisfy the conditions of a constrained optimum. This results in an order of magnitude reduction in computer time compared with a more traditional approach. Good accuracy is obtained by segmenting the trajectory.

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confidence: 98%

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confidence: 99%

High-speed Computation of Ascent Trajectories within Iterative Loops Using Collocation Methods

Hempel¹

1974

AIAA Journal

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Application of an advanced trajectory optimization method to ramjet propelled missiles

Paris

Joosten

Fink

1980

Optim Control Appl Methods

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SUMMARYThe mission performance characteristics of ramjet-propelled missiles are highly dependent upon the trajectory flown. Integration of the trajectory profile with the ramjet propulsion system performance characteristics to achieve optimal missile performance is very complex. Past trajectory optimization methods have been extremely problem dependent and require a high degree of familiarity to achieve success. A general computer code (CTOP) has been applied to ramjet-powered missiles to compute open-loop optimal trajectories. CTOP employs Chebyshev polynomial representations of the states and controls. This allows a transformation of the continuous optimal control problem to one of parameter optimization. With this method, the trajectory boundary conditions are always satisfied. State dynamics and path constraints are enforced via penalty functions. The presented results include solutions to minimum fuel-to-climb, minimumtime-to-climb, and minimum time-to-target intercept problems

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Numerical Solution on Parallel Processors of Two-Point Boundary-Value Problems of Astrodynamics

Miel

1990

Numerical Solution of Integral Equations

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Approximations of Interplanetary Trajectories by Chebyshev Series

Cited by 5 publications

References 2 publications

High-speed Computation of Ascent Trajectories within Iterative Loops Using Collocation Methods

High-speed Computation of Ascent Trajectories within Iterative Loops Using Collocation Methods

Application of an advanced trajectory optimization method to ramjet propelled missiles

Numerical Solution on Parallel Processors of Two-Point Boundary-Value Problems of Astrodynamics

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