Abstract : The approximate method of London and Seban for predicting the solidification rate and for melting in or around slabs, cylinders, and spheres has been reformulated in genral orthogonal curvilinear coordinates. Closed-form solutions are presented for the rate of phase change and temperature drop as a function of a nondimensional time, STeFo (product of Stefan and Fourier numbers), for various geometries including elliptic cylinders, spheroids of varying eccentricites, and bicylindrical problems. Both convection and flux boundary conditions which can vary with time are considered. The effect of Biot number on phase change times and the resulting boundary temperature are presented in graphical form for some of the geometries considered. The method's degree of approximation is investigated by comparison with published analytical results. The approximate applicability of the equations to some special phase change conduction problems is demostrated. (Author)
{"title":"Phase Change Heat Conduction in General Orthogonal Curvilinear Coordinates.","authors":"Leon Bledjian","doi":"10.2514/6.1979-181","DOIUrl":"https://doi.org/10.2514/6.1979-181","url":null,"abstract":"Abstract : The approximate method of London and Seban for predicting the solidification rate and for melting in or around slabs, cylinders, and spheres has been reformulated in genral orthogonal curvilinear coordinates. Closed-form solutions are presented for the rate of phase change and temperature drop as a function of a nondimensional time, STeFo (product of Stefan and Fourier numbers), for various geometries including elliptic cylinders, spheroids of varying eccentricites, and bicylindrical problems. Both convection and flux boundary conditions which can vary with time are considered. The effect of Biot number on phase change times and the resulting boundary temperature are presented in graphical form for some of the geometries considered. The method's degree of approximation is investigated by comparison with published analytical results. The approximate applicability of the equations to some special phase change conduction problems is demostrated. (Author)","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1979-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126591835","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1966-05-04DOI: 10.1016/B978-1-4832-2716-0.50056-6
J. Morenoff
{"title":"Communications in Orbit: A Legal Analysis and Prognosis","authors":"J. Morenoff","doi":"10.1016/B978-1-4832-2716-0.50056-6","DOIUrl":"https://doi.org/10.1016/B978-1-4832-2716-0.50056-6","url":null,"abstract":"","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"86 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1966-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126044725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1966-05-04DOI: 10.1016/B978-1-4832-2716-0.50042-6
D. Werts
{"title":"Establishment and Maintenance of a Communication Satellite System","authors":"D. Werts","doi":"10.1016/B978-1-4832-2716-0.50042-6","DOIUrl":"https://doi.org/10.1016/B978-1-4832-2716-0.50042-6","url":null,"abstract":"","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1966-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121510872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Publisher Summary This chapter describes the limiting orbits at the equilateral centers of libration. The planar restricted problem of three bodies is presented by the Hamiltonian function. For all these mass ratios, the limiting orbits have exhibited nontrivial characteristic exponents of the stable type. This result is somewhat puzzling. It has been suggested that the limiting orbits could perhaps be identified with that doubly asymptotic periodic orbit, which is the homoclinic solution common to the two manifolds of asymptotic solutions generated at the unstable equilibrium point. The fact that the limiting orbits have characteristic exponents of the stable type makes it embarrassing to accept this conjecture. Once the existence of limiting periodic orbits has been established, one can face the second part of Browns hypothesis. Each limiting orbit for a fixed value of the mass ratio μ should be the head of two families of periodic librations and for the first family, the period would decrease together with the Jacobi constant, whereas for the second family, the period would increase together with the Jacobi constant.
{"title":"Limiting orbits around the equilateral centers of libration","authors":"A. Deprit","doi":"10.1086/109859","DOIUrl":"https://doi.org/10.1086/109859","url":null,"abstract":"Publisher Summary This chapter describes the limiting orbits at the equilateral centers of libration. The planar restricted problem of three bodies is presented by the Hamiltonian function. For all these mass ratios, the limiting orbits have exhibited nontrivial characteristic exponents of the stable type. This result is somewhat puzzling. It has been suggested that the limiting orbits could perhaps be identified with that doubly asymptotic periodic orbit, which is the homoclinic solution common to the two manifolds of asymptotic solutions generated at the unstable equilibrium point. The fact that the limiting orbits have characteristic exponents of the stable type makes it embarrassing to accept this conjecture. Once the existence of limiting periodic orbits has been established, one can face the second part of Browns hypothesis. Each limiting orbit for a fixed value of the mass ratio μ should be the head of two families of periodic librations and for the first family, the period would decrease together with the Jacobi constant, whereas for the second family, the period would increase together with the Jacobi constant.","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1966-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128405249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1965-09-13DOI: 10.1016/B978-1-4832-2729-0.50012-0
A. Bennett
{"title":"Analytical Determination of Characteristic Exponents","authors":"A. Bennett","doi":"10.1016/B978-1-4832-2729-0.50012-0","DOIUrl":"https://doi.org/10.1016/B978-1-4832-2729-0.50012-0","url":null,"abstract":"","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"169 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123832118","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1965-09-13DOI: 10.1016/B978-1-4832-2729-0.50020-X
Bernard A. Glassman, Virginia C. Zvonkovich
{"title":"Parameter Hunting Procedures","authors":"Bernard A. Glassman, Virginia C. Zvonkovich","doi":"10.1016/B978-1-4832-2729-0.50020-X","DOIUrl":"https://doi.org/10.1016/B978-1-4832-2729-0.50020-X","url":null,"abstract":"","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"109 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124673134","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1965-09-13DOI: 10.1016/B978-1-4832-2729-0.50011-9
Lynn E. Wolaver
{"title":"Effect of Initial Configurations on Libration Point Motion","authors":"Lynn E. Wolaver","doi":"10.1016/B978-1-4832-2729-0.50011-9","DOIUrl":"https://doi.org/10.1016/B978-1-4832-2729-0.50011-9","url":null,"abstract":"","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121170518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1965-09-13DOI: 10.1016/B978-1-4832-2729-0.50019-3
A. G. Lubowe
{"title":"Efficient and Accurate Orbit Prediction for Very Long Periods of Time","authors":"A. G. Lubowe","doi":"10.1016/B978-1-4832-2729-0.50019-3","DOIUrl":"https://doi.org/10.1016/B978-1-4832-2729-0.50019-3","url":null,"abstract":"","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127506074","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1965-09-13DOI: 10.1016/B978-1-4832-2729-0.50010-7
J. Breakwell, R. Pringle
{"title":"Resonances Affecting Motion Near the Earth-Moon Equilateral Libration Points","authors":"J. Breakwell, R. Pringle","doi":"10.1016/B978-1-4832-2729-0.50010-7","DOIUrl":"https://doi.org/10.1016/B978-1-4832-2729-0.50010-7","url":null,"abstract":"","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"22 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125321676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 1965-09-13DOI: 10.1016/B978-1-4832-2729-0.50018-1
B. Lange, B. Parkinson
{"title":"Error Equations of Inertial Navigation with Special Application to Orbital Determination and Guidance","authors":"B. Lange, B. Parkinson","doi":"10.1016/B978-1-4832-2729-0.50018-1","DOIUrl":"https://doi.org/10.1016/B978-1-4832-2729-0.50018-1","url":null,"abstract":"","PeriodicalId":276120,"journal":{"name":"Progress in Astronautics and Rocketry","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1965-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123257606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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