16.07 Dynamics Fall 2009 Version 2.0 Lecture L29 - 3D Rigid Body Dynamics 3D Rigid Body Dynamics: Euler Angles The difficulty of describing the positions of the body-fixed axis of a rotating body is approached through the use of Euler angles: spin ψ˙, nutation θ and precession φ shown below in Figure 1. In this case we. Solution Features. Safe, Effective, and Accurate Temperature Measurement. ±0.3° C Temperature Measurement (with blackbody). Contactless and Fast Multi-person Screening. Recommended for Use in Commercial Buildings, Healthcare Facilities, Airports, Metro Stations, and Public Gathering Locations Human Body Temperature Measurement. I want solution manual for this text book.An Introduction to Management Science Quantitative Approaches to Decision Making, by D. Martin Thirteen Edition 2011 South Western, Cengage Learning, ISBN 13 978-1-4390-4323 -3. I want solution manual for this text book.An Introduction to Management Science Quantitative Approaches to Decision Making, by D. Martin Thirteen Edition 2011 South Western, Cengage Learning, ISBN 13 978-1-4390-4323 -3. Objective 2: To educate students to identify, formulate and solve engineering problems in rigid body dynamics. 2.1 Students will demonstrate the ability to isolate rigid bodies and to draw clear and appropriate free body diagrams. 2.2 Students will demonstrate an ability to identify kinematic and kinetic knowns and unknowns.
In this chapter we will consider the motion of solid objects under the application of forces and torques.We call these solid objects ``Rigid Bodies'.Of course nothing is completely rigid.Objects deform elastically, but these deformation are negligible for a wide range of problems.
For a rigid body, we will find in the equations that the motion can be separated into the motion of the center of massand the rotation around the center of mass.
In the rigid body limit, the state of a body can be described by six variables.These are the position of the center of mass andthree angles to describe the orientation of the object.
We will apply some of the results we have derived for transformation from an inertial frame to a rotating frame.For now we choose the body to be at rest inside the rotating (body) frameand the origin to be at the center of mass.
For the purposes of calculation, we will assume that the body is made up of a set of discrete masses,labeled by an index .In any inertial frame, the velocity of one of those masses is
In this equation, the is given in the inertial frame, is the velocity of the center of mass of the object,and is the position of the mass in the body frame in which it is at rest.
In introductory physics courses, we have learned about the moment of inertia and found that rotational motion is analogous to simple kinetics,with the analog of momentum being angular momentum andthe analog of the kinetic energy equation being .Thinking about the rotational physics of a dumbbell, we can see that rotational motion is not always so simple.Think about rotation of a dumb-ell about an axis at an angle to the axis.We find that the angular momentum is always perpendicular to the axis and thus is not parallel to .
Charles Stark Draper is shown below with a gyroscope used for the inertial guidance systems.
These were gyroscopes capable of measuring orientation on three angles plus accelerometers.The motion of a rocker could be measured and integrated to guide it to its target.By the time of the Minuteman missile, accuracies of 100m could be achieved on a 10000 km flight.Better accuracy can now be achieved with GPS.
Subsections- The Inertia Tensor
- Principal Axes
- Euler's Equations