Equations of Motion of a Cycloid [ deriving the parametric equations ]

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  • เผยแพร่เมื่อ 23 ม.ค. 2025

ความคิดเห็น • 88

  • @PackSciences
    @PackSciences 5 ปีที่แล้ว +36

    They see me rollin'
    They hatin'
    Patrolling and tryin' to catch me ridin' dirty
    Tryin' to catch me ridin' dirty
    Tryin' to catch me ridin' dirty
    Tryin' to catch me ridin' dirty
    Tryin' to catch me ridin' dirty
    My music's so loud
    I'm swangin'
    They hopin that they gonna catch me ridin' dirty
    Tryin' to catch me ridin' dirty
    Tryin' to catch me ridin' dirty
    Tryin' to catch me ridin' dirty
    Tryin' to catch me ridin' dirty
    Police think they can see me lean
    I'm tint so it ain't easy to be seen
    When you see me ride by they can see the glean
    And my shine on the deck and the TV screen
    Ride with a new chick, she like "hold up"
    Next to the Playstation controller is a full clip and my pistola
    Turn a jacker into a coma
    Girl you ain't know, I'm crazy like Krayzie Bone
    Just tryin'…

  • @pranayvenkatesh8815
    @pranayvenkatesh8815 5 ปีที่แล้ว +31

    You can derive this using electromagnetism. A particle, on being acted upon by a Lorentz force will show a cycloidal motion.

    • @Ricocossa1
      @Ricocossa1 5 ปีที่แล้ว +1

      Constant E and B perpendicular too each other yes. And it doesn't stop at one revolution, it keeps drawing cycloids!

    • @arjunverma963
      @arjunverma963 3 ปีที่แล้ว

      isn't it helical

    • @siddharthamondal4346
      @siddharthamondal4346 3 ปีที่แล้ว

      @@arjunverma963 Nope

    • @cool5763
      @cool5763 3 ปีที่แล้ว +3

      @@arjunverma963 you maybe jee aspirant like me, brother, in case the velocity is zero, and e perpendicular to b then it's cycloid(not in 12th boards syllabus though it's in jee adv syllabus) but when there is velocity and e,b perpendicular then it's helical path

  • @46pi26
    @46pi26 5 ปีที่แล้ว +9

    1:04 god tier trajectory drawing

  • @david-yt4oo
    @david-yt4oo 5 ปีที่แล้ว +10

    1:10 surprisingly, that is pretty good

  • @woonggyujin9653
    @woonggyujin9653 5 ปีที่แล้ว +17

    peculiar how the path of a cycloid, if oriented correctly, gives us the path that minimizes the time taken for an object to slide from one end to another (the Brachistochrone curve)

    • @MathPhysicsEngineering
      @MathPhysicsEngineering 3 ปีที่แล้ว

      I made a video that actually mentions this, and references to a particular scene in spiderman 2:
      th-cam.com/video/AzExth9AseQ/w-d-xo.html&ab_channel=Math%2CPhysics%2CEngineering

  • @radiuscubed
    @radiuscubed 4 ปีที่แล้ว +1

    Wow that's the pretty quick way of doing it. I did it by using Snell's Law to derive a differential equation (gets the same one gets for the cycloid) then solved it as a cycloid to get the parametric equations.

  • @dectorey7233
    @dectorey7233 5 ปีที่แล้ว +1

    This was explained so much better than when I learned it, ty :)

  • @david-yt4oo
    @david-yt4oo 5 ปีที่แล้ว +3

    actually, the whole thing was so good

  • @ianmathwiz7
    @ianmathwiz7 5 ปีที่แล้ว +3

    While you're on cycloids, you should derive the cycloid equation as an (analytic continuation of a) solution to the matter-dominated FLRW equations.

    • @Ricocossa1
      @Ricocossa1 5 ปีที่แล้ว +1

      Oh man I didn't know that! Too bad we don't live in such a universe. Heat death is way too boring. Cycloid universe sounds more fun. XD

  • @atlasinvestmentresearch5397
    @atlasinvestmentresearch5397 ปีที่แล้ว

    just think that one day we will lose this knowledge and rediscover the same equation over and over again. kind of make me feel gratitude that we come this far than one day it all need to be rediscover again. how fickle human in regard to advance knowledge

  • @jadegrace1312
    @jadegrace1312 5 ปีที่แล้ว +3

    Okay, this is epic

  • @walterlane5069
    @walterlane5069 4 ปีที่แล้ว

    I find a nice coralation with the principals of the cycloid and the curved path an airplane makes as the shortest distance from two points

  • @yoavshati
    @yoavshati 5 ปีที่แล้ว +2

    Can you use this to get y=f(x)?
    I tried differentiating with respect to the parameter to get dy/dx and then using x and y to replace the parameter derivative, and then solve it like a differential equation

    • @SmoothOutcomes
      @SmoothOutcomes 2 ปีที่แล้ว +1

      did you ever manage to do this? I need to work it out 😅

    • @yoavshati
      @yoavshati 2 ปีที่แล้ว

      @@SmoothOutcomes I'll try it when I get home

  • @yuma5297
    @yuma5297 5 ปีที่แล้ว +3

    can we get some stuff about linear alegebra ? some basic stuff and so

    • @dectorey7233
      @dectorey7233 5 ปีที่แล้ว +1

      Dr. Peyam is also doing an excellent series on Linear Algebra right now

    • @Gold161803
      @Gold161803 5 ปีที่แล้ว

      Came here to suggest both of these things

  • @David-km2ie
    @David-km2ie 5 ปีที่แล้ว +1

    What is the best book for self-learning complex analysis? Rigor prefered. Thx ;)

  • @morganmitchell4017
    @morganmitchell4017 5 ปีที่แล้ว +2

    Papa, why do you say 'theta' and write 'v'??? At 7:10

    • @apolloniuspergus9295
      @apolloniuspergus9295 5 ปีที่แล้ว

      That's another way to write theta.

    • @Gameboygenius
      @Gameboygenius 5 ปีที่แล้ว +2

      It's a curly theta. Explained below with a virgin/chad meme.
      i.imgur.com/K8sCSur.png

    • @morganmitchell4017
      @morganmitchell4017 5 ปีที่แล้ว +1

      @@Gameboygenius Fair enough! I'll start using it; don't want to be a virgin fukboi.

  • @goutamaggarwal2249
    @goutamaggarwal2249 ปีที่แล้ว

    Can anybody please tell me what kind of software can be used to trace the path of a point or create animations like the one in the video from 10-14 sec?

  • @DaveHelios99
    @DaveHelios99 4 ปีที่แล้ว

    You took theta to be in the first quadrant, but if i take theta to be, let's say, in the second one, some signs would be different, and so would be the equation of the cycloid. How do you explain that?

  • @glaurung78
    @glaurung78 ปีที่แล้ว

    At 8:07 do you say "same Spiel down here"?

  • @EpicGamer-wn9uu
    @EpicGamer-wn9uu 5 ปีที่แล้ว +1

    Can you do more videos on number theory? Such as linear modulo congruences and maybe polynomial modulo congruences?

  • @MrBenten867
    @MrBenten867 5 ปีที่แล้ว +2

    Papa's rolling over the floor

    • @MrBenten867
      @MrBenten867 5 ปีที่แล้ว

      @@PapaFlammy69 hey papa this is your boi from India I am 15 years old and I love all your videos would love to see more mechanics video like the rope falling down thank you

  • @bogdancorobean9270
    @bogdancorobean9270 5 ปีที่แล้ว +12

    Your theta looks like a v :(

    • @bogdancorobean9270
      @bogdancorobean9270 5 ปีที่แล้ว

      Oh, ok. Must be one of those fancy mathematician symbols, I've never heard of it..

  • @colinweaver2097
    @colinweaver2097 5 ปีที่แล้ว +34

    Um it’s pronounced gif honey...

  • @Loliver47
    @Loliver47 3 ปีที่แล้ว +1

    bro you cant even imagine how in love i am with you right now

  • @XanderGouws
    @XanderGouws 5 ปีที่แล้ว +9

    I love how 90% of these comments are people either roasting you about how you pronounce GIF, or how you write Greek letters lul

  • @Gameboygenius
    @Gameboygenius 5 ปีที่แล้ว +13

    It's pronounced Jeff.

    • @youtuberdisguiser6075
      @youtuberdisguiser6075 5 ปีที่แล้ว

      it'S pronounce gif with a hard g.

    • @korayacar1444
      @korayacar1444 5 ปีที่แล้ว

      TH-camr Disguiser r/woooosh

    • @Gameboygenius
      @Gameboygenius 5 ปีที่แล้ว

      @@youtuberdisguiser6075 No, I'm pretty sure I'm right. I learnt it from an episode of Jeffpardy where the answer was "The pronunciation of Jeff" and the question was "What is Jeff?"

    • @timothyaugustine7093
      @timothyaugustine7093 5 ปีที่แล้ว

      No it's pronounced 'give' with a hard g.

  • @zeeshanchaudhry3324
    @zeeshanchaudhry3324 5 ปีที่แล้ว

    Could you do a video on Viète's formula for the calculation of pi and how it relates to the geometry of a circle? Thank you for your time.

  • @philidor9657
    @philidor9657 5 ปีที่แล้ว

    Papa Flammy can you do a video on Fourier Series?

  • @Shailendra2819962
    @Shailendra2819962 5 ปีที่แล้ว

    I love these braingasmic videos

  • @pranjaldas1762
    @pranjaldas1762 5 ปีที่แล้ว

    You are soooooooooooooooooooooooo9ooooo brilliant

  • @DELTASERPENT
    @DELTASERPENT 5 ปีที่แล้ว

    Please neat hand writing

  • @jonbovi-69
    @jonbovi-69 8 หลายเดือนก่อน

    please do rolling ellipse this time.

  • @Ricocossa1
    @Ricocossa1 5 ปีที่แล้ว

    Mmh good. Now find that the cycloid is brachiatochrone in a uniform force field by taking the variation of the total time w.r. to q(t)

  • @XanderGouws
    @XanderGouws 5 ปีที่แล้ว +2

    These look familiar ;)

  • @jemcel0397
    @jemcel0397 5 ปีที่แล้ว

    Cool intro btw

  • @hendrik2765
    @hendrik2765 5 ปีที่แล้ว

    Hey that’s pretty good

  • @albertyeung5787
    @albertyeung5787 ปีที่แล้ว

    excellent

  • @Robinson8491
    @Robinson8491 2 ปีที่แล้ว

    I don't get it but you're great

  • @architsharma9836
    @architsharma9836 5 ปีที่แล้ว

    Don't remind me of this cycloid Iam studying this in engineering drawing.🔥🔥

  • @demonhunter4709
    @demonhunter4709 5 ปีที่แล้ว

    Great😊

  • @felipemagno569
    @felipemagno569 5 ปีที่แล้ว

    Jesus Christ I saw this last week in class...

    • @XanderGouws
      @XanderGouws 5 ปีที่แล้ว

      What class was it?

  • @omkarsinghchauhan3053
    @omkarsinghchauhan3053 5 ปีที่แล้ว

    nice

  • @physicsbhakt7571
    @physicsbhakt7571 ปีที่แล้ว

    1000th like

  • @huzynhaznhadhan5652
    @huzynhaznhadhan5652 4 ปีที่แล้ว

    Symbol sometime mke math complicated

  • @atrimandal4324
    @atrimandal4324 5 ปีที่แล้ว

    Knock knock

    • @atrimandal4324
      @atrimandal4324 5 ปีที่แล้ว

      I was gonna make a knock knock joke but papa gave me no love :(

    • @atrimandal4324
      @atrimandal4324 5 ปีที่แล้ว

      @@PapaFlammy69 Daisy

    • @atrimandal4324
      @atrimandal4324 5 ปีที่แล้ว

      Daisy who? Why of course it's DAISY ME ROLLLIN', THEY HATIN😂😂🌼

  • @Invalid571
    @Invalid571 5 ปีที่แล้ว

    Geef!

  • @jemcel0397
    @jemcel0397 5 ปีที่แล้ว

    Cool intro btw