Visualizing Rotations and Composition of Rotations with Rodrigues' Vector

The purpose of this paper is to show that the mathematical treatment of three dimensional rotations can be simplified, and its geometrical understanding improved, by using the Rodrigues' vector representation. We present a novel geometrical interpretation of the Rodrigues' vector. Based on this interpretation and simple geometrical considerations, we derive Euler Rodrigues' formula, Cayley's rotation formula, and the composition law for finite rotations. The level of this discussion should be suitable for undergraduate physics or engineering courses where rotations are discussed.Comment: 12 pages, 7 figure

Mosses from the Mascarenes - 7 : a small collection from Rodrigues

Fifteen taxa of mosses are reported from the island of Rodrigues. The second African report of Luisierella barbula (Schwaegr.) Steere bridges the Asian and New World disjunctions of this taxon. Three other species are reported new to the Mascarenes, i.e., Calymperes tenerum C.Müller var. tenerum, Fissidens ramulosus Mitten and Weissia edentula Mitten. Three are new to Rodrigues, i.e., Bryum truncorum Bridel, Fissidens sciophyllus Mitten and Vesicularia ayresii (Schimper ex Besch.) Broth

Connections between real polynomial solutions of hypergeometric-type differential equations with Rodrigues formula

Starting from the Rodrigues representation of polynomial solutions of the general hypergeometric-type differential equation complementary polynomials are constructed using a natural method. Among the key results is a generating function in closed form leading to short and transparent derivations of recursion relations and an addition theorem. The complementary polynomials satisfy a hypergeometric-type differential equation themselves, have a three-term recursion among others and obey Rodrigues formulas. Applications to the classical polynomials are given.Comment: 13 pages, no figure

More on F versus t tests for unit roots when there is no trend

Rodrigues and Tremayne (2004) interpret a problematic size result in a Monte Carlo study reported in Elder and Kennedy (2001) as arising from Elder and Kennedy's use of an inappropriate testing equation. In expositing their result, Rodrigues and Tremayne inadvertently lead readers to believe that the Elder and Kennedy conclusion is in error. We clarify the Rodrigues and Tremayne contribution, putting the validity of the Elder and Kennedy result in proper perspective and underlining the important role played by the starting value in Monte Carlo analyses.

Rodrigues formulas for the Macdonald polynomials

We present formulas of Rodrigues type giving the Macdonald polynomials for arbitrary partitions through the repeated application of creation operators on the constant 1. Three expressions for the creation operators are derived one from the other. When the last of these expressions is used, the associated Rodrigues formula readily implies the integrality of the (q,t)-Kostka coefficients. The proofs given in this paper rely on the connection between affine Hecke algebras and Macdonald polynomialsComment: 15 pages, AmsLaTe