Author: Robert Stawell BallPublisher:
ISBN:
Category : Algebra
Languages : en
Pages : 584
Book Description
A Treatise on the Theory of Screws
Author: Robert Stawell BallPublisher:
ISBN:
Category : Algebra
Languages : en
Pages : 584
Book Description
A Treatise on the Theory of Screws
Author: Robert Stawell BallPublisher: CUP Archive
ISBN:
Category : Kinematics
Languages : en
Pages : 588
Book Description
Treatise On the Theory of Screws
Author: Ball Robert S.Publisher:
ISBN: 9780259624561
Category :
Languages : en
Pages :
Book Description
A Treatise on the Theory of Screws
Author: Sir Robert Stawell BallPublisher:
ISBN: 9781429700313
Category :
Languages : en
Pages :
Book Description
Proceedings of the Royal Irish Academy
Author: Royal Irish AcademyPublisher:
ISBN:
Category : Astronomy
Languages : en
Pages : 486
Book Description
The Transactions of the Royal Irish Academy
Author: Royal Irish AcademyPublisher:
ISBN:
Category : Science
Languages : en
Pages : 868
Book Description
The Screw Calculus and Its Applications in Mechanics
Author: F. M. DimentbergPublisher:
ISBN:
Category : Kinematics
Languages : en
Pages : 180
Book Description
Nature
Author: Kinematic Geometry of Surface Machining
Author: Stephen P. RadzevichPublisher: CRC Press
ISBN: 1420063413
Category : Technology & Engineering
Languages : en
Pages : 538
Book Description
The principle of Occam's razor loosely translates tothe simplest solution is often the best. The author of Kinematic Geometry of Surface Machining utilizes this reductionist philosophy to provide a solution to the highly inefficient process of machining sculptured parts on multi-axis NC machines. He has developed a method to quickly calcu
Grassmann Algebra Volume 1: Foundations
Author: John BrownePublisher: John M Browne
ISBN: 1479197637
Category : Mathematics
Languages : en
Pages : 589
Book Description
Grassmann Algebra Volume 1: Foundations Exploring extended vector algebra with Mathematica Grassmann algebra extends vector algebra by introducing the exterior product to algebraicize the notion of linear dependence. With it, vectors may be extended to higher-grade entities: bivectors, trivectors, … multivectors. The extensive exterior product also has a regressive dual: the regressive product. The pair behaves a little like the Boolean duals of union and intersection. By interpreting one of the elements of the vector space as an origin point, points can be defined, and the exterior product can extend points into higher-grade located entities from which lines, planes and multiplanes can be defined. Theorems of Projective Geometry are simply formulae involving these entities and the dual products. By introducing the (orthogonal) complement operation, the scalar product of vectors may be extended to the interior product of multivectors, which in this more general case may no longer result in a scalar. The notion of the magnitude of vectors is extended to the magnitude of multivectors: for example, the magnitude of the exterior product of two vectors (a bivector) is the area of the parallelogram formed by them. To develop these foundational concepts, we need only consider entities which are the sums of elements of the same grade. This is the focus of this volume. But the entities of Grassmann algebra need not be of the same grade, and the possible product types need not be constricted to just the exterior, regressive and interior products. For example quaternion algebra is simply the Grassmann algebra of scalars and bivectors under a new product operation. Clifford, geometric and higher order hypercomplex algebras, for example the octonions, may be defined similarly. If to these we introduce Clifford's invention of a scalar which squares to zero, we can define entities (for example dual quaternions) with which we can perform elaborate transformations. Exploration of these entities, operations and algebras will be the focus of the volume to follow this. There is something fascinating about the beauty with which the mathematical structures that Hermann Grassmann discovered describe the physical world, and something also fascinating about how these beautiful structures have been largely lost to the mainstreams of mathematics and science. He wrote his seminal Ausdehnungslehre (Die Ausdehnungslehre. Vollständig und in strenger Form) in 1862. But it was not until the latter part of his life that he received any significant recognition for it, most notably by Gibbs and Clifford. In recent times David Hestenes' Geometric Algebra must be given the credit for much of the emerging awareness of Grassmann's innovation. In the hope that the book be accessible to scientists and engineers, students and professionals alike, the text attempts to avoid any terminology which does not make an essential contribution to an understanding of the basic concepts. Some familiarity with basic linear algebra may however be useful. The book is written using Mathematica, a powerful system for doing mathematics on a computer. This enables the theory to be cross-checked with computational explorations. However, a knowledge of Mathematica is not essential for an appreciation of Grassmann's beautiful ideas.