Finding Energy of the Slant Helix Strip by Using Classic Energy Methods on Joachimsthal Theorem
Issue:
Volume 6, Issue 3-1, June 2017
Pages:
1-5
Received:
15 February 2017
Accepted:
16 February 2017
Published:
6 March 2017
DOI:
10.11648/j.pamj.s.2017060301.11
Downloads:
Views:
Abstract: There are two forms of mechanical energy-potential energy and kinetic energy in physics. Potential energy Ep is stored energy of position. The amount of kinetic energy Ek possesed by a moving object is depent upon mass and speed. The total mechanical energy possesed by an object is the sum of its kinetic and potential energies. Now we calculate the mathematical physic on Joachimsthal Theorem. In this paper, we find the eneryg of two curves on different surfaces and slant helix strips by using classic energy formulaes in Euclidean Space E3.
Abstract: There are two forms of mechanical energy-potential energy and kinetic energy in physics. Potential energy Ep is stored energy of position. The amount of kinetic energy Ek possesed by a moving object is depent upon mass and speed. The total mechanical energy possesed by an object is the sum of its kinetic and potential energies. Now we calculate the...
Show More
An Introduction to Differential Geometry: The Theory of Surfaces
Kande Dickson Kinyua,
Kuria Joseph Gikonyo
Issue:
Volume 6, Issue 3-1, June 2017
Pages:
6-11
Received:
6 February 2017
Accepted:
14 February 2017
Published:
13 May 2017
DOI:
10.11648/j.pamj.s.2017060301.12
Downloads:
Views:
Abstract: From a mathematical perspective, a surface is a generalization of a plane which does not necessarily require being flat, that is, the curvature is not necessarily zero. Often, a surface is defined by equations that are satisfied by some coordinates of its points. A surface may also be defined as the image, in some space of dimensions at least three, of a continuous function of two variables (some further conditions are required to insure that the image is not a curve). In this case, one says that one has a parametric surface, which is parametrized by these two variables, called parameters. Parametric equations of surfaces are often irregular at some points. This is formalized by the concept of manifold: in the context of manifolds, typically in topology and differential geometry, a surface is a manifold of dimension two; this means that a surface is a topological space such that every point has a neighborhood which is homeomorphic to an open subset of the Euclidean plane. A parametric surface is the image of an open subset of the Euclidean plane by a continuous function, in a topological space, generally a Euclidean space of dimension at least three. The paper aims at giving an introduction to the theory of surfaces from differential geometry perspective.
Abstract: From a mathematical perspective, a surface is a generalization of a plane which does not necessarily require being flat, that is, the curvature is not necessarily zero. Often, a surface is defined by equations that are satisfied by some coordinates of its points. A surface may also be defined as the image, in some space of dimensions at least three...
Show More
