Robust Continuous Collision Detection Between
... 2. Collision detection between arbitrary polyhedra During a simulation multiple polyhedra can usually move simultaneously. However, for the described algorithm the polyhedra are assumed to be moving separately, one by one, for short periods of time. Therefore the collision detection problem is redu ...
... 2. Collision detection between arbitrary polyhedra During a simulation multiple polyhedra can usually move simultaneously. However, for the described algorithm the polyhedra are assumed to be moving separately, one by one, for short periods of time. Therefore the collision detection problem is redu ...
Rotational motion of rigid bodies
... The definition of ω is written in this form (and not as ω =dχ/dt) since the function χ(t) that could be differentiated over time does not exist, in general. General rotations are not described by a single rotation vector because as the body rotates, the direction of the rotation axis changes, too. T ...
... The definition of ω is written in this form (and not as ω =dχ/dt) since the function χ(t) that could be differentiated over time does not exist, in general. General rotations are not described by a single rotation vector because as the body rotates, the direction of the rotation axis changes, too. T ...
Patellar Tracking in Primary Total Knee
... used as a landmark, as rotational and angular deformities below the knee commonly exist. One common technique is to adjust tibial component rotation with the knee at 90º to optimize geometric mating of the tibial component to the femoral component. This technique prioritizes femoral-tibial component ...
... used as a landmark, as rotational and angular deformities below the knee commonly exist. One common technique is to adjust tibial component rotation with the knee at 90º to optimize geometric mating of the tibial component to the femoral component. This technique prioritizes femoral-tibial component ...
Chapter 3 Vectors
... Many aspects of physics involve a description of a location in space. In Chapter 2, for example, we saw that the mathematical description of an object’s motion requires a method for describing the object’s position at various times. This description is accomplished with the use of coordinates, and i ...
... Many aspects of physics involve a description of a location in space. In Chapter 2, for example, we saw that the mathematical description of an object’s motion requires a method for describing the object’s position at various times. This description is accomplished with the use of coordinates, and i ...
12 Matrices - Games @ UCLAN
... will see that matrices are used to perform this transformation: the world, view and projection matrices. You will also see that the matrices can be combined into a single matrix that carries out all of the maths in one operation. There are calls within DirectX to do all of the operations. You n ...
... will see that matrices are used to perform this transformation: the world, view and projection matrices. You will also see that the matrices can be combined into a single matrix that carries out all of the maths in one operation. There are calls within DirectX to do all of the operations. You n ...
Chapter 9 Rigid Body Motion in 3D - RIT
... Consider an arbitrary rigid object and a set of xyz axes. Our first task will be to find the moment of inertia about an axis passing through the origin but oriented in an arbitrary direction, not one of the coordinate axes. The line is bidirectional, but once we set the object into rotation the vect ...
... Consider an arbitrary rigid object and a set of xyz axes. Our first task will be to find the moment of inertia about an axis passing through the origin but oriented in an arbitrary direction, not one of the coordinate axes. The line is bidirectional, but once we set the object into rotation the vect ...
Chapter 8 - HCC Learning Web
... Example 8.3 Balancing act A woman of mass m=55.0 kg sits on the left end of a seesaw a plank of length L=4.00 m, pivoted in the middle as in figure 8.8. (a) First compute the torques on the seesaw about an axis that passes through the pivot point. Where should a man of mass M=75.0 kg sit if the sys ...
... Example 8.3 Balancing act A woman of mass m=55.0 kg sits on the left end of a seesaw a plank of length L=4.00 m, pivoted in the middle as in figure 8.8. (a) First compute the torques on the seesaw about an axis that passes through the pivot point. Where should a man of mass M=75.0 kg sit if the sys ...
Solving Simultaneous Equations and Matrices
... could be specified by stating the values for and . The convention for working in 2D is to indeed define two vectors, denoted by and which are used in exactly the same context as the vectors and to allow any point in a 2D plane to be specified by a pair of numbers equivalent to the scalar values and ...
... could be specified by stating the values for and . The convention for working in 2D is to indeed define two vectors, denoted by and which are used in exactly the same context as the vectors and to allow any point in a 2D plane to be specified by a pair of numbers equivalent to the scalar values and ...
Lecture notes
... Homogeneous Transform Advantages • Unified view of transformation as matrix multiplication – Easier in hardware and software ...
... Homogeneous Transform Advantages • Unified view of transformation as matrix multiplication – Easier in hardware and software ...
Static Equilibrium
... • The net torque is about an axis through any point in the xy plane • Does it matter which axis you choose for calculating torques? • NO. The choice of an axis is arbitrary • If an object is in translational equilibrium and the net torque is zero about one axis, then the net torque must be zero abou ...
... • The net torque is about an axis through any point in the xy plane • Does it matter which axis you choose for calculating torques? • NO. The choice of an axis is arbitrary • If an object is in translational equilibrium and the net torque is zero about one axis, then the net torque must be zero abou ...
ComCMePr2c
... The explanation of surplus of perihelion rotation of the Sun oblateness now is complicated with complexities of model of interaction and absence of knowledge of distribution of the Sun density on radius and along an axis of the Sun. Therefore the executed calculations of influence of the Sun oblate ...
... The explanation of surplus of perihelion rotation of the Sun oblateness now is complicated with complexities of model of interaction and absence of knowledge of distribution of the Sun density on radius and along an axis of the Sun. Therefore the executed calculations of influence of the Sun oblate ...
Document
... Big Idea is simple: The axis is the only thing that defines the direction of rotation ...
... Big Idea is simple: The axis is the only thing that defines the direction of rotation ...
Kite stability criteria
... own. If the kite is rotating then the side area in front of the centre of rotation is moving to one side and being resisted by a force generated by Fig.5 Sideforce due the local sideslip. The side area behind the centre of rotation is moving the to sideslip other way and being resisted by a force in ...
... own. If the kite is rotating then the side area in front of the centre of rotation is moving to one side and being resisted by a force generated by Fig.5 Sideforce due the local sideslip. The side area behind the centre of rotation is moving the to sideslip other way and being resisted by a force in ...
File - Phy 2048-0002
... 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, ...
Dear David Weber
... The formula (4) gives speed velocity of perihelion rotation of Mercury orbit relatively motionless space is equal 582.05 arcsec/century for 1950.0 and 583.15 for 2000.0 [4]. It is velocity of perihelion rotation according to observation. Due to orbits elements by J.L. Simon et al. [3] it is equal 58 ...
... The formula (4) gives speed velocity of perihelion rotation of Mercury orbit relatively motionless space is equal 582.05 arcsec/century for 1950.0 and 583.15 for 2000.0 [4]. It is velocity of perihelion rotation according to observation. Due to orbits elements by J.L. Simon et al. [3] it is equal 58 ...
phys1443-spring11
... rotational axis is the same as the axis of symmetry. However if the axis of rotation does not coincide with axis of symmetry, the calculation can still be done in a simple manner using parallel-axis theorem. I I CM MD 2 y ...
... rotational axis is the same as the axis of symmetry. However if the axis of rotation does not coincide with axis of symmetry, the calculation can still be done in a simple manner using parallel-axis theorem. I I CM MD 2 y ...
Vectors - Lecture`s of computer graphics
... The tail of vector s is attached to the head of vector r. The resultant vector t = r + s is defined by adding the corresponding components of r and s together. In subtraction , the components of vector s are reversed to produce an equal and opposite vector ...
... The tail of vector s is attached to the head of vector r. The resultant vector t = r + s is defined by adding the corresponding components of r and s together. In subtraction , the components of vector s are reversed to produce an equal and opposite vector ...
Rotational Motion Torque Moment of Inertia
... ular to the door s hinges. You will ac force near the doo When a force is to rotate about th axis is measured b but we will consid Chapter 11. Consider the wr perpendicular to t ...
... ular to the door s hinges. You will ac force near the doo When a force is to rotate about th axis is measured b but we will consid Chapter 11. Consider the wr perpendicular to t ...
Document
... Hamilton’s principle [principe van Hamilton] states that the time evolution of the system, x (t), corresponds to a stationary point of the action, Eq. 4. More precisely, of all the curves x (t) with given start point x (t1 ) = x1 and given end point x (t2 ) = x2 the true solution is a stationary poi ...
... Hamilton’s principle [principe van Hamilton] states that the time evolution of the system, x (t), corresponds to a stationary point of the action, Eq. 4. More precisely, of all the curves x (t) with given start point x (t1 ) = x1 and given end point x (t2 ) = x2 the true solution is a stationary poi ...
PHYS 1443 * Section 501 Lecture #1
... What does The father away the particle is from the rotation axis, the more radial this tell you? acceleration it receives. In other words, it receives more centripetal force. Total linear acceleration is Thursday, June 30, 2011 ...
... What does The father away the particle is from the rotation axis, the more radial this tell you? acceleration it receives. In other words, it receives more centripetal force. Total linear acceleration is Thursday, June 30, 2011 ...
Rotational motion is all around us
... car, a CD in its player, a pirouetting ice skater, all rotate. b. In this chapter, we consider rotation about an axis that is fixed in space, as in a merry-go-round, or about an axis that is moving without changing its direction in space, as in a rolling wheel on a car that is traveling in a straigh ...
... car, a CD in its player, a pirouetting ice skater, all rotate. b. In this chapter, we consider rotation about an axis that is fixed in space, as in a merry-go-round, or about an axis that is moving without changing its direction in space, as in a rolling wheel on a car that is traveling in a straigh ...
Chapter 10: Dynamics of Rotational Motion
... For points not lying in XY plane, the position vectors have components in Z-direction as well as in X- and Y-directions. This gives the angular momentum of each particle a component perpendicular to Z-axis. But if Z-axis is the axis of symmetry, components for particles on opposite sides of this ax ...
... For points not lying in XY plane, the position vectors have components in Z-direction as well as in X- and Y-directions. This gives the angular momentum of each particle a component perpendicular to Z-axis. But if Z-axis is the axis of symmetry, components for particles on opposite sides of this ax ...
Document
... speed, in which a cylindrical rotor can rotate about the axis going through its center and perpendicular to the cross – section area of the rotator. Initially, the angular velocity is ω0 0 . After 300 s the speed reached 18000 r/min. it is known that the angular acceleration a of the rotation is p ...
... speed, in which a cylindrical rotor can rotate about the axis going through its center and perpendicular to the cross – section area of the rotator. Initially, the angular velocity is ω0 0 . After 300 s the speed reached 18000 r/min. it is known that the angular acceleration a of the rotation is p ...
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.