#mechanics

mkwadee@diasp.eu

I was explaining to my wife how the #velocity #components of an idealized #projectile differ. She was having some problems understanding that only the #vertical component changes and that the #horizontal component remains constant. In the end, I knocked up this little animation to tr and explain pictorially (the program in #WxMaxima is actually interactive. so you can stop it, step through it or run it backwards if that helps).

#Maths #Mathematics #Mechanics #ConstantAcceleration #Vectors #Dynamics #MyWork #CCBYSA #FreeSoftware

mkwadee@diasp.eu

It's straightforward to calculate the #components of a #2D #vector given that you have a pre-defined set of #axes. Often, we talk about #cartesian #coordinates. If the vector changes, whether in #magnitude or #direction, we can calculate the updated components too. The converse question is what if the the vector is held constant and you change or #rotate the axes? The components in the new coordinate system can be found with a little bit of #trigonometry and #algebra. As vectors are #first-order #tensors, they are much simpler to calculate than quantities like stress for which I've also made an animation for if you search for the hashtag #tensors.

In this animation, you can see the components changing as the axes go through a full rotation.

#MyWork #CCBYSA #Mathematics #Mechanics

mkwadee@diasp.eu

In #SolidMechanics, #stress has some counter-intuitive properties, particularly when you rotate the coordinate system. The values of normal and shear stress transform according to the rules of #second-order #tensors, which is a step above #vectors (first-order tensors). To avoid always having to use #matrix #algebra to find the components, #engineers and #mathematicians have long used the Mohr's circle to evaluate them. This is a very handy tool and allows you to find the new values by using circular geometry instead.

Here, I've used #WxMaxima to create this #animation.

#Mechanics #Mathematics #Engineering #MohrsCircle #FreeSoftware

mkwadee@diasp.eu

In the #2D #elasticity, #equilibrium of #stresses can be represented on an infinitesimal rectangular element with components of both #DirectStress and #ShearStress generally acting on all four edges. If you were to rotate the rectangle, the stresses change in a precisely orchestrated fashion. In the orientation where the shear stress components vanish, we get what are called #PrincipalStresses and they and their directions can be ascertained precisely through #eigenvalue analysis. This little graphical demonstration shows one example of such a state. The #AnimatedGif was produced a routine written in #WxMaxima.

#Mathematics #TheoryOfElasticity #Mechanics #SolidMechanics #Engineering #MyWork #CCBYSA #WorkInProgress

sylviaj@joindiaspora.com

Noam Chomsky - The 5 Filters of the Mass Media Machine

https://www.youtube.com/watch?v=34LGPIXvU5M

' #AmyGoodman narrates a short video piece based on #NoamChomsky’s #book#ManufacturingConsent”, a seminal work on #mainstream #journalism and its role in the #mechanics of #power.' According to #Chomsky, media operate through #5 #filters: #ownership, #advertising, the #media #elite, #flak and the #common #enemy. #analysis #propaganda #machine #msm #profit #freedom #democracy