3 Dimensional Rotational Model

as a response to http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=2084.0

reference: http://en.wikipedia.org/wiki/Gimbal_lock

Gimbal lock is the loss of one degree of freedom in a three-dimensional space that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space.

The word lock is misleading: no gimbal is restrained. All three gimbals can still rotate freely about their respective axes of suspension. Nevertheless, because of the parallel orientation of two of the gimbals axes there is no gimbal available to accommodate rotation along one axis.

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3 Dimensional Rotational Model

Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of mass, known as pitch, roll and yaw.

Description:

The 3 Dimensional Rotational Model is a setup that resembles an actual real life demonstration set using to illustrate and allow exploration of the meaning of pitch, roll and yaw. There are 2 possible frames to choose from cylinder rings or rectangles.

The independent axes when selected allows independent axes to be rotated without affecting the others 2 axes, while when independent is not selected allows a couple rotational model that could be used to explore the concept of gimbal lock.

In simple Java, the is no object rendered in the model, just the frames to explore pitch, roll and yaw.

In Java 3D, a aeroplane (in wrl) is rendered inside the model for better association to aeroplane pitch, roll and yaw angles in 3D.

Exercises:

Engage:

Have you wondered how do airplane pliots communicate to each other about the angles that the airplane makes with a defined equilibrium state?

Do you know that what you learn here can be applied to boat and ships angles too?

Set the sliders to roll = 90 , pitch 90 and yaw = 0 degree.

explore the roll slider and verify whether the following statement is appriopriate.

"The equilibrium roll angle is known as wings level or zero bank angle"

Discuss and suggest a value of roll for this zero bank angle to occur.

hint: roll = 90 degree

Similarly, explore the sliders pitch and yaw and visit http://en.wikipedia.org/wiki/Flight_dynamics_(aircraft) and other websites related to draw sketches and describe in sentence(s) the meaning of

i) roll

ii) pitch

iii) yaw

hint:

According to http://en.wikipedia.org/wiki/Gimbal_lock

Gimbal lock is the loss of one degree of freedom in a three-dimensional space that occurs when the axes of two of the three gimbals are driven into a parallel configuration, "locking" the system into rotation in a degenerate two-dimensional space.

Explore the model and discuss with your classmates what this means?

Advanced Learner:

Please submit your remix model that model features that are not available in the existing virtual lab and share your model with the world through NTNUJAVA Virtual Physics Laboratory http://www.phy.ntnu.edu.tw/ntnujava/index.php?board=28.0. Impacting the world with your model now.

Credits:

The 3D rotational Model was created by Fu-Kwun Hwang (original model found here http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=2084.0) , customized by Loo Kang WEE (newer model found here http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=2237.0) using the Easy Java Simulations (EJS) version 4.3.3.3 authoring and modeling tool. An applet version of this model is available on the NTNU website < http://www.phy.ntnu.edu.tw/ntnujava/ >.

You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open EJS Model" from the pop-up menu. You must, of course, have EJS installed on your computer. Information about EJS is available at: