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As shown in Figure 6, to determine the stress components (,) acting on a plane at an angle counterclockwise to the plane on which acts, we travel an angle in the same counterclockwise direction around the circle from the known stress point (,) to point (,), i.e., an angle between lines ¯ and ¯ in the Mohr circle. The double angle approach ...
These attitudes are specified with two angles. For a line, these angles are called the trend and the plunge. The trend is the compass direction of the line, and the plunge is the downward angle it makes with a horizontal plane. [15] For a plane, the two angles are called its strike (angle) and its dip (angle).
In geometry, an intersection is a point, line, or curve common to two or more objects (such as lines, curves, planes, and surfaces). The simplest case in Euclidean geometry is the line–line intersection between two distinct lines , which either is one point (sometimes called a vertex ) or does not exist (if the lines are parallel ).
Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.
If a cylinder is used in this sense, the above paragraph would read as follows: A plane section of a right circular cylinder of finite length [6] is a circle if the cutting plane is perpendicular to the cylinder's axis of symmetry, or an ellipse if it is neither parallel nor perpendicular to that axis. If the cutting plane is parallel to the ...
A pencil of planes, is the set of planes through a given straight line in three-space, called the axis of the pencil. The pencil is sometimes referred to as a axial-pencil [5] or fan of planes or a sheaf of planes. [6] For example, the meridians of the globe are defined by the pencil of planes on the axis of Earth's rotation.
The circle is obtained when the cutting plane is parallel to the plane of the generating circle of the cone; for a right cone, this means the cutting plane is perpendicular to the axis. If the cutting plane is parallel to exactly one generating line of the cone, then the conic is unbounded and is called a parabola.
To find the angle of a rotation, once the axis of the rotation is known, select a vector v perpendicular to the axis. Then the angle of the rotation is the angle between v and Rv. A more direct method, however, is to simply calculate the trace: the sum of the diagonal elements of the rotation matrix.