Search results
Results From The WOW.Com Content Network
In computational mechanics, a characteristic length is defined to force localization of a stress softening constitutive equation. The length is associated with an integration point. For 2D analysis, it is calculated by taking the square root of the area. For 3D analysis, it is calculated by taking the cubic root of the volume associated to the ...
Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path between the two points on the surface of the sphere. (By comparison, the shortest path passing ...
In the 3rd century BC, Archimedes, using a method resembling Cavalieri's principle, [5] was able to find the volume of a sphere given the volumes of a cone and cylinder in his work The Method of Mechanical Theorems. In the 5th century AD, Zu Chongzhi and his son Zu Gengzhi established a similar method to find a sphere's volume. [2]
List of moments of inertia. Moment of inertia, denoted by I, measures the extent to which an object resists rotational acceleration about a particular axis; it is the rotational analogue to mass (which determines an object's resistance to linear acceleration). The moments of inertia of a mass have units of dimension ML 2 ( [mass] × [length] 2).
The mass of any of the discs is the mass of the sphere multiplied by the ratio of the volume of an infinitely thin disc divided by the volume of a sphere (with constant radius ). The volume of an infinitely thin disc is π R 2 d x {\displaystyle \pi R^{2}\,dx} , or π ( a 2 − x 2 ) d x {\textstyle \pi \left(a^{2}-x^{2}\right)dx} .
In geometry, a sphere packing is an arrangement of non-overlapping spheres within a containing space. The spheres considered are usually all of identical size, and the space is usually three- dimensional Euclidean space. However, sphere packing problems can be generalised to consider unequal spheres, spaces of other dimensions (where the ...
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes. Important in navigation , it is a special case of a more general formula in spherical trigonometry , the law of haversines , that relates the sides and angles of spherical triangles.
For a larger sphere, the band will be thinner but longer. In geometry, the napkin-ring problem involves finding the volume of a "band" of specified height around a sphere, i.e. the part that remains after a hole in the shape of a circular cylinder is drilled through the center of the sphere. It is a counterintuitive fact that this volume does ...