Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is s...Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is solvable.In this article,the authors provide the set of all left-invariant minimal unit vector fields on the solvable Lie group Gn,and give the relationships between the minimal unit vector fields and the geodesic vector fields,the strongly normal unit vectors respectively.展开更多
The spatial orientation of optical radiation sources has long been the hot topic in the aerospace and the military applications.Current researches mainly focus on the high precision orientation on the partial field of...The spatial orientation of optical radiation sources has long been the hot topic in the aerospace and the military applications.Current researches mainly focus on the high precision orientation on the partial field of view.Thus,combination of several partial fields of view is required to achieve orientation when the field of view exceeds 180°,which results in the increase of size,weight,power consumption and the cost.By defining radiation energy and direction of the optical radiation source as a vector and applying the cosine law of radiation and vector theorem,it is shown that the vector can be obtained from unit normal vectors on the three un-coplanar surfaces and from the energy projected by the optical radiation source.Based on this,an orientation method with 360° full field of view by a polyhedron is suggested,the mathematical formula for anti-multipath interference is supposed and the error upper limit is derived.The feasibility and effectiveness of this method are validated by measurements and simulation.An accuracy better than 2.866° and 0.574° is achieved when the ratio of measurement error of energy on arbitrary surface and the true value are 5% and 1%,respectively,given the matrix composed of unit normal vectors on three measurement surfaces is orthogonal.展开更多
基金supported by the National Natural Science Foundation of China (Nos. 12001007,12201358)the Natural Science Foundation of Shandong Province (No. ZR2021QA051)+1 种基金the Natural Science Foundation of Anhui Province (No. 1908085QA03)Starting Research Funds of Shandong University of Science and Technology (Nos. 0104060511817, 0104060540626)
文摘Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is solvable.In this article,the authors provide the set of all left-invariant minimal unit vector fields on the solvable Lie group Gn,and give the relationships between the minimal unit vector fields and the geodesic vector fields,the strongly normal unit vectors respectively.
文摘The spatial orientation of optical radiation sources has long been the hot topic in the aerospace and the military applications.Current researches mainly focus on the high precision orientation on the partial field of view.Thus,combination of several partial fields of view is required to achieve orientation when the field of view exceeds 180°,which results in the increase of size,weight,power consumption and the cost.By defining radiation energy and direction of the optical radiation source as a vector and applying the cosine law of radiation and vector theorem,it is shown that the vector can be obtained from unit normal vectors on the three un-coplanar surfaces and from the energy projected by the optical radiation source.Based on this,an orientation method with 360° full field of view by a polyhedron is suggested,the mathematical formula for anti-multipath interference is supposed and the error upper limit is derived.The feasibility and effectiveness of this method are validated by measurements and simulation.An accuracy better than 2.866° and 0.574° is achieved when the ratio of measurement error of energy on arbitrary surface and the true value are 5% and 1%,respectively,given the matrix composed of unit normal vectors on three measurement surfaces is orthogonal.
