Spherical Coordinates 3D Animation
HTML-код
- Опубликовано: 14 окт 2024
- This section can be a little hard to visualize in 2D. This video should help you to visualize spherical coordinates and set up the bounds of integration for triple integrals.
Paul's Math Notes: tutorial.math.l...
I don't understand why they don't teach this today at my university without using animations like these to help us visualize 3D shapes mentally. We have the technology now...
I feel the same way. I made this because I couldn't find something similar. Most of your professors learned it from chalkboard drawings, so don't be too upset if they try to teach you the same way :)
@@XYZandRGBhow do you go about animating things like this ?
@@tommygstonymec I use Blender. I build all of the pieces you see in the video and vary their rotation and size and position using keyframes.
hmm
Maybe in the future generations they will use now animation or graphical representations using new technologies
A good teacher is one who can make complicated topics the most easiest ones. Thank you
Thank's a ton for the animation man, it really helped, like fr. My prof isn't the best, she runs through the material like she's tryna speedrun the class
Thanks dude saved my brains from frying
θ is to reduce the aggregate of three-dimensional space to a surface, Φ is to reduce the aggregate of a surface to a line, which is the intersection of the surface and the cone, and ρ is to reduce a line to a point. The positioning of any point in space can be completed.
Sending you all the best wishes, being able to explain difficult concepts easily is what marks a great educator. Thank you!
This is gold for spherical coordinates. Thank you!
Animations help a LOT. This video made the concept crystal clear to me. Thank you!
Thank you very much, i have an exam in an hour and finally understand about all of this
i have a re-exam and now phi is much more intuitive than the first time!! Thanks very very much for such a good explanation!!!!
I'm from INDIA Your video helped me a lot to make my concept crystal clear ❤
This video made me understand why theta is only from 0 to π, thanks!
ty for everything, my friend saw your video and he say he gonna take 5 in the impossible test tomorow, god bless him and all the students
this is marvelous effort to teach coordinates.
Great video. Cleared all my doubts. Thank you so much for this! 😁
*Great explanation Sir. Thanks, lots of love from India*
understood in a very easy way ...because you took lot of hard pain to do it. thanks a lot
very helpful video! i have a calculus coming up and you have no idea how this saved me hahah thanks a bunch 😊
Good luck on your exam!
Thanks so much for making this video. Unique and super helpful visualization!
Great animation.Thanks. You have my subscription. I think greatly of all the pre computer graphics mathematicians who could see it all in their heads.Makes one wonder? In the long run are our brains going to be less or more capable of visualisation?
That's such an interesting question. I feel like we are adding to the number of people that can visualize a topic each time we express it in a new way. There's no shortage of difficult concepts to understand, so I suppose anyone can still exercise the skill as much as they want.
I had a colleague suggest that some boys gain an advantage in spatial visualization over girls from jumping off of playground equipment and tracking movements of the ball in sports more often. I have no idea if nature or nurture is the main culprit, but I suspect it's a skill that can be strengthened.
Thanks
Nice video. I would recommend including the bounds and other numbers you're talking about on screen next time.
Thanks! Putting this (unfinished) video up was a little experiment to see if people would like this kind of video. Comments like yours motivate me to continue making them.
Thank you very much. It might have took some effort to make this video, I am grateful for this.
I actually appreciate your time, I had finally learnt.
thank you SO MUCH for this video. It got me unstuck. I didn't realize that the vertical angle goes only from 0 to Pi, not to 2Pi, like angles usually would
This was very concise! Illustrated fantastici! All important key features in order to calculate the transmitted irradience by angular dependent. Using Yours - presented coordinates and the following spherical coordinate system I can specify a given direction for the zenith and azimuth angles thus the transmittance of this system is a function of direction of incident radiation. So valuable information also for the irradience from the sun, sky and for all hemispheric areas given by the independent of changes in the sun or sky radiance. Thank you because performing an integration of the transmitted irradience and calculating the total radiant flux in civil engineering we can see better geometry for example water, glass, polarized elements, i. c. Also we can imply two-dimensional Fourier transform of Cartesian coordinates if we understand better first important step that implys in all disciplines not only engineering approach! 👏👏👏👏
Thank u so much Teacher Love from INDIA ❤
dude you're the boss, thank you !!
dude you're the best
Great video bro! I couldnt understand what phi is and now got it! Thank you!
a really nice representation thank you
did you mix up phi and theta? my notes and other videos show them the other way
It depends on which book you are using. There is no standard, but what I have in my video is what I've seen in Stewart calculus.
@@XYZandRGB its weird there is no standard. thanks
our professor is trying to teach this using a chalkboard its sooo frustrating,, thanku so much for posting this!
Short and simple but very helpful, thank you so much
this has been incredibly helpful, thank you!
saved my calc grade thank you🙏
Very intuitve explanation. Thanks 💯
Very informative and very well presented ,thank you
finally a good video regarding this !!! thank you !!!
Awesome explaination
makes learning so interesting
Thank you very much for the graph & explanation
Thanks so much for this video. It really clarified a few things for me.
Great explanation sir
wonderful
Thank you so much! this made it so clear
Great video
as in polar coordinate 2d we needed an initial line and pole for frame of reference , i wonder if we need all the three axes here?
Changing the frame of reference from what I described here is a bit more advanced than what I can cover here, but I would assume we need all 3 axes to define a frame of reference.
Thank you very much. 🙏
This helped me understand the Qubit
very good visuals
Nice explanation
Thank you very much 😍😍 !!
Please sir make more videos on multivariable calculus 😇
Great video, keep up the good work!!
Very good
great animations, can I ask how they were created?
I made them using Blender, a free 3D software
This was beautiful!! Thank you very much.
muchismas gracias por explicarlo todo bien! me ha ayudado mucho!
Thanks! This was extremely helpful :D
Thank you so much for sharing this video! It's very helpful!!
Thanks!
thank u so much you helped me a lot🌷💖
AMAZING IT WAS.... ❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️❤️
AMAZING VIDEO THANK YOU SO MUCH
Thank you! Also why did you change your audio of Phi out lol
I mistakenly said "theta" instead a few times. Audio editing is not my strong suit :)
So x and y axioms have an angular relationship and the z axioms phi is independent, having half the values because its the same on either side of the axis without concern with position. Hmm interesting stuff.
excellent
amazing video
the lovely grease pencil :) I am also planning to use Blender to do math animations. It's gonna be fun. Subs.
I actually used this site. www.calligraphr.com/en/
but I will probably be using grease pencil for that in the future.
Thank you so much. You saved me
cleared my doubt professor
great video 🙌🏾👏🏾
Can't theta be from π/2 to 3π/2 at 5:25 or it is same as π to 2π
theta is positive when it is measured counterclockwise rotation from x axis about z axis. I guess that might be the reason for it being in the range of π to 2π.
Remember that theta starts at the positive x-axis, just like polar coordinates. It's a little odd because it "looks" like it is starting on the left.
which software did you use to create animations?
I used Blender. It's free and getting better every version
Is fie not clockwise?
"fie" or phi originates from the positive z-axis, and it travels in all directions. To use an analogy, 11:00 and 1:00 on the clock would have the same phi value of 1 hour
which software are you using ?
I used Blender. It's totally free to use!
Wow, this helped a lot. Thank you
The question is when do we use normal triple integral(dz dy dz), triple integral in cylindrical coordinates (r dz dr dθ) or triple integral in spherical coordinates?
is it based on the graph or there is a better way of knowing this
""Given that sometimes we encounter functions that are hard to graph
I would suggest using the coordinate system that has the most constants in its bounds. You can convert the equation you are integrating to any coordinate system you like, so it is usually based on the shape of the solid.
thank you!
Thank you so much :)
Great video ! what is difference between Parametric and Cylindrical (r,theta,z)?
Cylindrical is a coordinate system very similar to spherical that uses (r, theta, and z) like you mentioned. r is measured in the same way as polar coordinates. Parametric is pretty different, and is usually used to define curves that travel along a 3D surface, rather than the solid itself. They can be used together to define a curve. For example:
r = 1, theta = t and z = t will give you a curve that will spiral up along the surface of a cylinder.
I need these animations! my prof's drawings are so hard to interpret
Wow beautifuly explained
LEGEND
amazing. Thanks a lot.
Thank you very much sir !!!
great video sir ... helped a lot
super helpful...thank u so much
Thank you
Thank you so much ❤
Nice video
thank you for this animation!!
Thank you !!
5:24 why theta limits are from pi to 2pi
Could you pls explain
Theta starts at the positive x axis, and moves toward the positive y axis, so it has to travel halfway around and start at pi.
cylindrical polar coordinates when parallel to x-axis
how can i solve something like this???
I would think about how you can redefine your variables. Instead of theta being related to x and y, have it related to y and z.
Keep the hard work up 👍
Thank you!! This was very informative
Good
Hello can i ask? Is it necessary to change the sign if we going to transform it to spherical coordinates?
Since r is a radius and goes in all directions in the XY plane, we don't need to worry about positives and negatives that can result from being "above" or "below" the axis.
awesome video!!
fi will be with x axis not theta
Your textbook may label them differently. This is how they are labelled in Stewart's Calculus.