and 270°. however, a clockwise rotation implies a negative magnitude, so a counterclockwise turn has a positive magnitude. there are specific rules for rotation in the coordinate plane. they are: type of rotation a point on the image a point on the image after rotation rotation of 90° (...
When we graph the line segment on acartesian plane, endpoint L ( 2, 5 ) is in Quadrant I while endpoint S ( -6, 8 ) is in Quadrant II. The new position of point L ( 2, 5 ), when rotated by 180 degrees clockwise or counterclockwise, is L’ ( -2, -5 ), while the new p...
An angle is made up of two rays sharing an endpoint. This shared endpoint is called thevertex. An angle is formed when a ray is rotated around the vertex or thecenter of rotation. The starting ray is called the initial side. In the Cartesian plane, the initial side is usually placed ...
The final orientations of the other axes depend on all three Euler angles. We now need the transformation matrices. The first rotation causes e^1′ and e^2′ to remain in the xy-plane, and has in its first two rows and columns exactly the same form as S in Eq. (3.25): (3.35)S1...
If a point (x,y)(x,y) on the Cartesian plane is represented on a new coordinate plane where the axes of rotation are formed by rotating an angle θθ from the positive x-axis, then the coordinates of the point with respect to the new axes are (x′,y′)(x′,y′). We can use...
This is a spherical, as opposed to Cartesian, representation of vectors. The convensions used in this toolbox are as follows:The elevation angle, theta, measures the rotation from the x-y plane to the point in question.The azimuth angle, psi, measures the rotation of the point from x ...
Stress vector acting on an arbitrary plane defined by the normal. Since the original body is in equilibrium, the pyramidal element has to be subjected to an equilibrated system of actions. The actions acting on the element are determined by integrating the traction vectors over the surface areas...
A pendulum with two degrees of freedom, a heavy point swinging in a vertical plane on a weightless spring was considered. The Cartesian coordinate system has the origin at point O, the load rest position. Axes x and y are directed along the vertical and the horizontal, respectively. The ...
The driving force behind developing the present research has been the derivation of the NURBS-based isogeometric analysis which will enable an elegant formulation of the plane Bernoulli–Euler beams, being a function only of the global rectangular Cartesian coordinates. The verification and accuracy of...
A“globally optimal” polynomial basis that would always outperform the others apparently does not exist. Among other reasons, this is because the recognition power depends not only on the chosen features (moments) but also on the data themselves. Most authors tend towards using orthogonal polynomial...