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... If we call the z axis the axis of rotation, angular velocity is defined by avg=/t, where is the angular displacement of a rotating object in the time t. Instantaneous angular velocity is =d/dt. ...
... If we call the z axis the axis of rotation, angular velocity is defined by avg=/t, where is the angular displacement of a rotating object in the time t. Instantaneous angular velocity is =d/dt. ...
ACSC330 - Computer Graphics
... where r is the distance of the point from the origin. Positive values of θ in these equations indicate a counterclockwise rotation, and negative values for θ rotate objects in a clockwise direction. Matrix Representations and Homogeneous Coordinates There are many applications that make use of the b ...
... where r is the distance of the point from the origin. Positive values of θ in these equations indicate a counterclockwise rotation, and negative values for θ rotate objects in a clockwise direction. Matrix Representations and Homogeneous Coordinates There are many applications that make use of the b ...
Chapter 4
... direction about the ray from the origin through the point (x, y, z). The angle parameter specifies the angle of rotation in degrees. ...
... direction about the ray from the origin through the point (x, y, z). The angle parameter specifies the angle of rotation in degrees. ...
Section 8-2 Center of Mass
... Section 8-2 Center of Mass 11. Center of Mass – point at which all of the mass of the body can be considered to be concentrated when analyzing transitional motion. a. Regular shaped objects (i.e. sphere, cube) center of mass is at the geometric center of the object. i. Different for oddly shaped ob ...
... Section 8-2 Center of Mass 11. Center of Mass – point at which all of the mass of the body can be considered to be concentrated when analyzing transitional motion. a. Regular shaped objects (i.e. sphere, cube) center of mass is at the geometric center of the object. i. Different for oddly shaped ob ...
Scene Graph, Hierarchical Data Structures and Quaternions
... Quaternion Interpolation • Quaternion and rotation matrix has a strict one-toone mapping (pp. 489, 3D Computer Graphics, Watt, 3rd Ed) • To achieve smooth interpolation of quaternion, need spherical linear interpolation (slerp), (on pp. 489-490, 3D Computer Graphics, Watt, 3rd Ed) – Unit quaternion ...
... Quaternion Interpolation • Quaternion and rotation matrix has a strict one-toone mapping (pp. 489, 3D Computer Graphics, Watt, 3rd Ed) • To achieve smooth interpolation of quaternion, need spherical linear interpolation (slerp), (on pp. 489-490, 3D Computer Graphics, Watt, 3rd Ed) – Unit quaternion ...
5. STATIC EQUILIBRIUM. Key words: Static Equilibrium, First
... Where r is the distance from the axis of rotation to the point where force F applied; F is the magnitude of the applied force; θ is the angle between the line of action of the force and a line connecting axis of rotation and the point at which the force is applied (see Fig. 5.1). Usually we will use ...
... Where r is the distance from the axis of rotation to the point where force F applied; F is the magnitude of the applied force; θ is the angle between the line of action of the force and a line connecting axis of rotation and the point at which the force is applied (see Fig. 5.1). Usually we will use ...
Chapter 8
... A student sits on a rotating stool holding two 3.0-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg • m2 and is assumed to be constant. T ...
... A student sits on a rotating stool holding two 3.0-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation, and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is 3.0 kg • m2 and is assumed to be constant. T ...
Chapter 10 – Rotation and Rolling
... Rigid body: body that can rotate with all its parts locked together and without shape changes. Rotation axis: every point of a body moves in a circle whose center lies on the rotation axis. Every point moves through the same angle during a particular time interval. Reference line: fixed in the body, ...
... Rigid body: body that can rotate with all its parts locked together and without shape changes. Rotation axis: every point of a body moves in a circle whose center lies on the rotation axis. Every point moves through the same angle during a particular time interval. Reference line: fixed in the body, ...
Polarimetry
... collection of achiral molecules, however, for any orientation of a molecule that changes the plane of polarization of the light, there is apt to be another molecule with a mirror-image orientation which has the opposite effect. Consequently, when a beam of plane-polarized light is passed through suc ...
... collection of achiral molecules, however, for any orientation of a molecule that changes the plane of polarization of the light, there is apt to be another molecule with a mirror-image orientation which has the opposite effect. Consequently, when a beam of plane-polarized light is passed through suc ...
Rotational Motion and Torque
... the rotational axis, an outside force must push / pull on the object to keep it spinning. Gravity is such a force that acts on the mass of an object by the mutual attraction between two objects due to the mass of each object and the distance between them. ...
... the rotational axis, an outside force must push / pull on the object to keep it spinning. Gravity is such a force that acts on the mass of an object by the mutual attraction between two objects due to the mass of each object and the distance between them. ...
Momentum
... concept of inertia and how it is a measure of an object’s desire to resist movement. It was a product of its mass. • Momentum is moving inertia. It is a product of not only an objects mass but also how fast it is moving (velocity) • Newton’s 1st law rewritten to include momentum • An object that is ...
... concept of inertia and how it is a measure of an object’s desire to resist movement. It was a product of its mass. • Momentum is moving inertia. It is a product of not only an objects mass but also how fast it is moving (velocity) • Newton’s 1st law rewritten to include momentum • An object that is ...
File - Mr. Tremper`s Webpage
... • If the force is perpendicular to the radius of rotation the lever arm is simply the distance from the axis • For the doorknob it is the distance from the hinges ...
... • If the force is perpendicular to the radius of rotation the lever arm is simply the distance from the axis • For the doorknob it is the distance from the hinges ...
Document
... evaluation, advice, diagnosis or treatment by a healthcare professional. You should speak to your physician or make an appointment to be seen if you have questions or concerns about this information or your medical condition. Viewer discretion is advised: Material may contain medical images that may ...
... evaluation, advice, diagnosis or treatment by a healthcare professional. You should speak to your physician or make an appointment to be seen if you have questions or concerns about this information or your medical condition. Viewer discretion is advised: Material may contain medical images that may ...
Lecture 23: Rigid Bodies
... Brian Mirtich and John Canny, ``Impulse-based Simulation of Rigid Bodies,'' in Proceedings of 1995 Symposium on Interactive 3D Graphics, April 1995. http://www.cs.berkeley.edu/~jfc/mirtich/papers/ibsrb.ps D. Baraff. Linear-time dynamics using Lagrange multipliers. Computer Graphics Proceedings, Annu ...
... Brian Mirtich and John Canny, ``Impulse-based Simulation of Rigid Bodies,'' in Proceedings of 1995 Symposium on Interactive 3D Graphics, April 1995. http://www.cs.berkeley.edu/~jfc/mirtich/papers/ibsrb.ps D. Baraff. Linear-time dynamics using Lagrange multipliers. Computer Graphics Proceedings, Annu ...
Circular Motion
... How would you simulate gravity by using Centripetal Force? Think about acceleration. Would the simulated gravitational force be the same in all areas of the space station? Why or why not? ...
... How would you simulate gravity by using Centripetal Force? Think about acceleration. Would the simulated gravitational force be the same in all areas of the space station? Why or why not? ...
Transformations - Studentportalen
... Vectors and matrices (2D) Translation x’andy’resultfroman additional independent factor ...
... Vectors and matrices (2D) Translation x’andy’resultfroman additional independent factor ...
Rotational Dynamics
... Force changes the velocity of a point object. In other words: a force that is exerted in a very specific way changes the angular velocity of an extended object. Extended object- an object that has a definite shape and size. There is an inverse relationship present here since to get the most effect ...
... Force changes the velocity of a point object. In other words: a force that is exerted in a very specific way changes the angular velocity of an extended object. Extended object- an object that has a definite shape and size. There is an inverse relationship present here since to get the most effect ...
rigid-body motion
... • state contains x, y, θ, vx, vy, ω • Have – F = ma (2 equations) – T = Iω – x = ∫vx dt – y = ∫vy dt – θ = ∫ω dt ...
... • state contains x, y, θ, vx, vy, ω • Have – F = ma (2 equations) – T = Iω – x = ∫vx dt – y = ∫vy dt – θ = ∫ω dt ...
Quaternions and spatial rotation
Unit quaternions, also known as versors, provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to rotation matrices they are more numerically stable and may be more efficient. Quaternions have found their way into applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics, orbital mechanics of satellites and crystallographic texture analysis.When used to represent rotation, unit quaternions are also called rotation quaternions. When used to represent an orientation (rotation relative to a reference coordinate system), they are called orientation quaternions or attitude quaternions.