Logarithmic Spiral: An Ideal Trajectory for the Interplanetary Vehicle with Engines of Low Sustained Thrust

Bacon, Ralph Hoyt

doi:10.1119/1.1934788

Cited by 49 publications

(27 citation statements)

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“…Tsu (1959), London (1960) and Bacon (1959) all investigated the only known exact analytical solution; the logarithmic spiral solution. Bacon's work was actually concerned with continuous thrust spacecraft, not specifically solar sails, although the results were directly applicable.…”

Section: Introductionmentioning

confidence: 99%

An analytical description of three-dimensional heliocentric solar sail orbits

Stewart

Palmer

Roberts

2016

Celest Mech Dyn Astr

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This paper introduces a simple analytical approximation to three-dimensional heliocentric solar sail orbits where the only forces considered are solar gravity and solar radiation. The approximation is based upon the previously studied hodograph transformation and provides a description of the inclination, longitude of ascending node and true latitude for a specific set of initial conditions. It is shown that the rotational symmetry of a heliocentric orbit allows this specific solution to be mapped onto a solution with arbitrary initial conditions. The approximation is then compared to the numerical results for a solar sail on an Earth escape trajectory with an area to mass ratio up to twice as high as current technology allows.

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Section: Introductionmentioning

confidence: 99%

An analytical description of three-dimensional heliocentric solar sail orbits

Stewart

Palmer

Roberts

2016

Celest Mech Dyn Astr

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“…A Logarithmic Spiral is a plane curve for which the angle between the radius vector and the tangent to the curve is a constant [14]. Such spirals can be approximated mathematically defined by the following equation on the 2-dimensional polar coordinate system   …”

Section: A the Logarithmic Spiralmentioning

confidence: 99%

Logarithmic Spiral-based Construction of RBF Classifiers

Guerfala¹,

Sifaoui²,

Abdelkrim³

2017

ijacsa

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Abstract-Clustering process is defined as grouping similar objects together into homogeneous groups or clusters. Objects that belong to one cluster should be very similar to each other, but objects in different clusters will be dissimilar. It aims to simplify the representation of the initial data. The automatic classification recovers all the methods allowing the automatic construction of such groups. This paper describes the design of radial basis function (RBF) neural classifiers using a new algorithm for characterizing the hidden layer structure. This algorithm, called k-means Mahalanobis distance, groups the training data class by class in order to calculate the optimal number of clusters of the hidden layer, using two validity indexes. To initialize the initial clusters of k-means algorithm, the method of logarithmic spiral golden angle has been used. Two real data sets (Iris and Wine) are considered to improve the efficiency of the proposed approach and the obtained results are compared with basic literature classifier

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“…In Sect. 9.1 we recover the tangential thrust profile that Bacon (1959) related to the logarithmic spiral and formulate the dynamics. The first reason for recovering the logarithmic spiral is how simple the thrust profile is.…”

Section: Discussionmentioning

confidence: 99%

“…Bacon (1959) and Tsu (1959) explored the equations of motion for the case of logarithmic spirals, the latter considering the use of solar sails. However, the flight-path angle is constant along a logarithmic spiral so they turn out not to be practical for trajectory design.…”

Section: Discussionmentioning

confidence: 99%

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Regularization in Astrodynamics: applications to relative motion, low-thrust missions, and orbit propagation = Regularización en Astrodinámica: aplicaciones al movimiento relativo, misiones de bajo empuje, y propagación de órbitas

Vicens¹

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Logarithmic Spiral: An Ideal Trajectory for the Interplanetary Vehicle with Engines of Low Sustained Thrust

Abstract: It is shown that a vehicle with engines of low sustained thrust can be directed along a logarithmic spiral through an inverse-square gravitational field by means of an extremely simple guidance system; it is possible to choose a spiral for which initial and final velocities are optimum.

Cited by 49 publications

References 0 publications

An analytical description of three-dimensional heliocentric solar sail orbits

An analytical description of three-dimensional heliocentric solar sail orbits

Logarithmic Spiral-based Construction of RBF Classifiers

Regularization in Astrodynamics: applications to relative motion, low-thrust missions, and orbit propagation = Regularización en Astrodinámica: aplicaciones al movimiento relativo, misiones de bajo empuje, y propagación de órbitas

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