The emergence of the geometric field from the kinetic term can be made clearer in the vicinity of the origin where the following Taylor expansion of the induced metric in normal coordinates applies: [g.sub.ij] = [[delta].sub.ij] - (1/3)[R.sub.ikjl] [x.sup.k] [x.sup.l] + O([[absolute value of x].sup.3]) (in fact, Riemann used the expansion of a metric in normal coordinates to originally define the curvature tensor; in normal coordinates there is no necessity to distinguish between co- and contravariant indices; see [26, 27]), and expanding the square root of the determinant of the metric yields
van de Ven, "A closed formula for the Riemann normal coordinate expansion," General Relativity and Gravitation, vol.
It is clearly seen from papers [12, 13], where examples of a free falling hydrogen atom is considered and the Fermi normal coordinates
Suppose that modal analysis theory still can be used to solve (6) considering strain dependence of hard coating, and normal mode shape matrix always indicates constant value for the different strain states of composite plate; thus the relation between physical coordinates and normal coordinates can be expressed as
where q is the response in normal coordinate and [[PHI].sub.N] is normal mode shape matrix, which can be obtained from the following equation:
where [omega] refers to excitation angular frequency, [K.sup.*.sub.N] refers to complex stiffness matrix in normal coordinate, and [C.sub.N] refers to damping matrix in normal coordinate.
To establish relations between the equations of flow and the spillway geometry, the normal coordinates
system of the flow is expressed as Cartesian coordinate system.
The initial layout of the graph is called the normal view of the graph, and its coordinates are called normal coordinates. Vertices are graphically represented by shapes whose bounding boxes are square (chosen arbitrarily).
Finally, each vertex in fisheye view is assigned a visual worth (VW), computed based on its distance from the focus (in normal coordinates) and its API.
The position of vertex v in the fisheye view is a function of its position in normal coordinates and the position of the focus f: