When you said, “we are all grownups here.” My first thought was no I’m not, and then I realized that I’m 18 as of a few days ago and I can’t believe that hit me while watching a classical two-body problem.
@@DotPhysics I currently bought a book called (Fundamentals of Astrodynamics 2nd edition) by Roger R. Bate and 3 more writers Can you tell me if I bought a right book or not
@@DotPhysics Einstein never nearly understood the mechanism of gravity. Einstein never nearly understood what is gravity. Einstein never nearly understood TIME. Einstein never nearly understood what is E=MC2. I have surpassed Einstein and Newton. FACTS. The coronal heating problem in solar physics relates to the question of why the temperature of the Sun's corona is millions of kelvins versus the thousands of kelvins of the surface. I have solved the problem. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/as) GRAVITATIONAL force/ENERGY, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). This CLEARLY explains what is E=MC2 AND F=MA ON BALANCE. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !! What is E=MC2 IS dimensionally consistent. What is GRAVITY IS, ON BALANCE, AN INTERACTION that cannot be shielded or blocked. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE). Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution. “Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/AS what is BALANCED electromagnetic/gravitational force/ENERGY, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! Magnificent. Consider WHAT IS THE SUN ON BALANCE !!!! THINK. Consider why and how that there is something instead of nothing ON BALANCE. Consider what is THE EYE ON BALANCE. The first, second, AND third dimensions in/of/AS SPACE are BALANCED !!! (Consider TIME AND time dilation ON BALANCE !!!) The stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). I have CLEARLY explained, ON BALANCE, how and why a given PLANET (including what is THE EARTH) sweeps out equal area in equal TIME. Great. By Frank Martin DiMeglio
@@DotPhysics What is the Sun ON BALANCE, AND how is the Sun's CORONA understood (ON BALANCE)? HOW CAN (AND DOES) WHAT IS THE SUN EXIST IN BOTH TIME AND SPACE?: What is the Sun is fully consistent WITH what is E=MC2 in accordance WITH what are SPACE AND TIME. Indeed, what is E=MC2 IS dimensionally consistent. What is GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. Indeed, consider what is outer “space” ON BALANCE; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! INDEED, the stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! GREAT. I have explained the coronal heating ON BALANCE !!!! The Sun's corona is one, TWO, AND three dimensional gravitational/electromagnetic SPACE (ON/IN BALANCE) consistent WITH what is E=MC2 !!!! Therefore, c squared CLEARLY (AND NECESSARILY) represents a dimension of SPACE ON BALANCE !!!! Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! Therefore, ON BALANCE, a given PLANET (including what is THE EARTH) sweeps out equal area in equal TIME. Accordingly, stellar clustering ALSO proves, ON BALANCE, that ELECTROMAGNETISM/energy is gravity. Consider what is THE EYE ON BALANCE !!!!! The stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! c squared CLEARLY represents a dimension of SPACE ON BALANCE !!!! TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! I have mathematically (AND CLEARLY) proven and explained what is the fourth dimension ON BALANCE !!!! Perfect. It ALL CLEARLY makes perfect sense ON BALANCE !!!!! INDEED, consider why and how that there is something instead of nothing ON BALANCE !!!!! GREAT. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! By Frank Martin DiMeglio The answer is that the corona is one, two, AND three dimensional SPACE ON/IN BALANCE. It is fully consistent WITH what is E=MC2. It is pure ENERGY on balance with what is the Sun. It is a balanced SPACE, without which (again, ON BALANCE) what is the Sun could not exist or be manifest. Great. INDEED, TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Consider what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE !! The rotation of WHAT IS THE MOON matches the revolution, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). The stars AND PLANETS are POINTS in the night sky ON BALANCE. Great. “Mass”/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/AS what is BALANCED electromagnetic/gravitational force/ENERGY, AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE); AS GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !!! GREAT. By Frank Martin DiMeglio
OMG I finally figure out the two body problem,thank you sooooo much.your video is always very logical and understandable. I’m so glad to find your channel.
This is an amazing video. I think this derivation was probably outside the scope of what I was looking for but I got so excited at the end when you got the orbits to work and created that effective potential plot. I definitely want to try this in my free time. Using the numerical method you used, would it be possible to do something similar to this for 3 bodies or more and how hard would to show the orbits on screen, if not all the bodies are in the same orbital plane?
@@lulwahabduljabbar You can't analytically but you can numerically. I did it using the Runge-Kutta method not to long ago but that isn't the best numerical method for something like this.
To add to my comment about elliptical orbits. The Lagrangian T=T-U=1/2MR'*2+1/2^r'*2-U(r) when you assume R's velocity is constant it oversimplifies and ignores the acceleration I want to isolate. If r vector is oscillating with a sin wave acceleration the center of mass has to be oscillating with m/M*sin wave acceleration. The system is going to get the potential to a minimum. This is the mechanism that induces entropy. We need to add a component that equates the loss of acceleration in the bodies with the loss of change in potential energy. This is a very important fundamental mechanism of energy. If we solve for the acceleration of R can you, we isolate a clean answer.
at 42:52 there must be a wrong formula for F2 - when we divide norm(r) by mag(r)**2 this is no longer inverse square law. That norm(r) seems inappropriate because as far as i know it does the same as mag(r).
I have been working on a derivation of the acceleration on the center of mass that you hold to zero in order to constrain the system. In an elliptical orbit the gravitational force and centrifugal force are out of balance and the imbalance is in one direction. The force exerted on the center of mass is not zero. Some of the acceleration in the orbiting body must be transferred to the orbited body, conservation of energy requires it. This would mean an elliptical orbit slowly accelerates the whole system and forms a stable circular orbit given sufficient time. This is the mechanism that keeps the solar system intact. At the point you apply the Lagrange, instead of holding the acceleration of the center of mass to zero how about isolating the acceleration in the large mass. I have what I think is the answer 1/2ma=MA, a is the acceleration added to a circular orbit to induce an elliptical orbit. 1/2 comes from the final stable circular orbit being the mean velocity between the two orbits. This makes the formation of the solar system completely different. this is also the basis I will propose a unified theory. Give me a clean derivation and we could win a Nobel. Rip L Martin
At 11:25, you mention that the potential energy function U(r) only takes in "r" as in the relative position between the two masses, and not R as the position of the center of mass. Why does the potential energy only depend on the relative location between the two bodies? Thank you :)
When you wrote the Lagrangian, is r the distance the objects are from each other? Also, may this discussion extend to (classical) scattering? Also, do you have another video that explains why certain objects are in orbits (whether periodic or not) while some objects collide? I’m finding these mechanics to be difficult.
What is the physical interpretation of the minimum in the potential plot? Does it imply that the net force is 0? Because the derivative of the potential wrt r should be 0 for a critical point (aka the net force). So does that imply that F_centrifugal = F_real?
It's been a while since I looked at this, so here are two answers that might not be the best. 1) In Lagrangian mechanics, if you have a generalized coordinate (q_i), then the partial of L wrt to q-dot is the generalized momentum. In this case, we just call that the angular momentum 2) In general, we know that the partial of L wrt theta-dot is a constant. We can just pick that constant to be l and the units work out as angular momentum
@@DotPhysics Thanks, that clears things up! I had another small question. At 23:35, when you take the partial of the Lagrangian with respect to theta, you equate it to 0. I know this is because you assume every variable is constant but isn't theta dot dependent on theta? So differentiating with respect to theta should not imply that theta dot is 0 right? Its like differentiating a velocity function with respect to position, it wouldn't be 0(?) My knowledge in multivariable calc is limited thats why this question may seem strange but hope u can help me through that.
Ok, I've spent two days straight on this, and I still don't get it. How am I supposed to "update the momentum" that you say to do at 28 minutes. If I just want to do a 'simple' upwards ball throw from Earth at the speed of say 10km/s, without any angles or atmosphere, and with the mass of the ball irrelevant for the center mass, I have arrived that my starting equation is: 10,000x-((6.67*10^-11)*(5.97*10^24)/((6.37*10^6+distance traveled(0))^2)0.5x^2=10,000x-4.9x^2, which is a basic parabola. And in order to find out where the ball is in ten minutes, I can certainly manually subtract x=1 from 10,000, plug the result into the distance, and repeat the whole process six hundred times, but I understand calculus was designed to help with that? The links to the equations provided don't work (Ug is not defined At or near line 37: U=Ug+Uc) and (v1cirle is not defined At or near line 17: star1.v=vector(0,v1cirle,0)) and I wouldn't know how to code anyway. Any explanations I can find online either assume the gravity remains constant, try to complicate the problem with a bunch of stuff like the rocket exhaust, talk about vectors, or just kinda... assume I guess that I'd know how to update the momentum. And maybe if I went though the whole calculus curriculum again I'd find it obvious, but I really don't. I would appreciate the help.
You always solve the EL equations for all of your generalized coordinates to retrieve the equations of motion. In this case, the generalized coordinates are r and theta
@ 1:11 HERE'S MY PROBLEM: don't show a 2D x,y-plan if you want to describe a 3D situation. It is not even the plane in which these objects orbit! @ 4:25 It's nothing but the dot-product of the two r-dot vectors. He doesn't explain it too ... despite all his talking. I give up here. Bye.
7:51 when I pause the video, it is miserable, that the TH-cam overlay appears and blocks the important reading of the formula! I need the pause to let the formula "sit in"!! is there any option to turn overlay off/on, when I want? Also the TH-cam-font, like so many others, are miserable/confusing: iI1lLoO0t | C() the small l should have a "bent foot" while the small t doesn't need it, as long as it is clearly distinguisable from + !!! Other fonts play around with unnecesssary serifes, whilst still not resolving the unambiguity problem.
When you said, “we are all grownups here.” My first thought was no I’m not, and then I realized that I’m 18 as of a few days ago and I can’t believe that hit me while watching a classical two-body problem.
Happy Solar Orbit Day! Also, welcome to the adult table. It's fun.
@@DotPhysics I currently bought a book called (Fundamentals of Astrodynamics 2nd edition) by
Roger R. Bate and 3 more writers
Can you tell me if I bought a right book or not
@@DotPhysics Einstein never nearly understood the mechanism of gravity. Einstein never nearly understood what is gravity. Einstein never nearly understood TIME. Einstein never nearly understood what is E=MC2. I have surpassed Einstein and Newton. FACTS.
The coronal heating problem in solar physics relates to the question of why the temperature of the Sun's corona is millions of kelvins versus the thousands of kelvins of the surface.
I have solved the problem. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE).
Inertia/INERTIAL RESISTANCE is proportional to (or BALANCED with/as) GRAVITATIONAL force/ENERGY, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). This CLEARLY explains what is E=MC2 AND F=MA ON BALANCE. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !! What is E=MC2 IS dimensionally consistent. What is GRAVITY IS, ON BALANCE, AN INTERACTION that cannot be shielded or blocked. Gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE). Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution. “Mass"/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/AS what is BALANCED electromagnetic/gravitational force/ENERGY, AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! Magnificent.
Consider WHAT IS THE SUN ON BALANCE !!!! THINK. Consider why and how that there is something instead of nothing ON BALANCE. Consider what is THE EYE ON BALANCE. The first, second, AND third dimensions in/of/AS SPACE are BALANCED !!! (Consider TIME AND time dilation ON BALANCE !!!) The stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). I have CLEARLY explained, ON BALANCE, how and why a given PLANET (including what is THE EARTH) sweeps out equal area in equal TIME. Great.
By Frank Martin DiMeglio
@@DotPhysics What is the Sun ON BALANCE, AND how is the Sun's CORONA understood (ON BALANCE)?
HOW CAN (AND DOES) WHAT IS THE SUN EXIST IN BOTH TIME AND SPACE?:
What is the Sun is fully consistent WITH what is E=MC2 in accordance WITH what are SPACE AND TIME. Indeed, what is E=MC2 IS dimensionally consistent. What is GRAVITY IS, ON BALANCE, an INTERACTION that cannot be shielded or blocked. Indeed, consider what is outer “space” ON BALANCE; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! INDEED, the stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! GREAT. I have explained the coronal heating ON BALANCE !!!! The Sun's corona is one, TWO, AND three dimensional gravitational/electromagnetic SPACE (ON/IN BALANCE) consistent WITH what is E=MC2 !!!! Therefore, c squared CLEARLY (AND NECESSARILY) represents a dimension of SPACE ON BALANCE !!!! Accordingly, ON BALANCE, the rotation of WHAT IS THE MOON matches the revolution; AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!! Therefore, ON BALANCE, a given PLANET (including what is THE EARTH) sweeps out equal area in equal TIME. Accordingly, stellar clustering ALSO proves, ON BALANCE, that ELECTROMAGNETISM/energy is gravity. Consider what is THE EYE ON BALANCE !!!!! The stars AND PLANETS are POINTS in the night sky ON BALANCE !!!! c squared CLEARLY represents a dimension of SPACE ON BALANCE !!!! TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!! I have mathematically (AND CLEARLY) proven and explained what is the fourth dimension ON BALANCE !!!! Perfect. It ALL CLEARLY makes perfect sense ON BALANCE !!!!! INDEED, consider why and how that there is something instead of nothing ON BALANCE !!!!! GREAT. TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE) !!!!
By Frank Martin DiMeglio
The answer is that the corona is one, two, AND three dimensional SPACE ON/IN BALANCE. It is fully consistent WITH what is E=MC2. It is pure ENERGY on balance with what is the Sun. It is a balanced SPACE, without which (again, ON BALANCE) what is the Sun could not exist or be manifest. Great. INDEED, TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). Consider what is the fully illuminated (AND setting/WHITE) MOON ON BALANCE !! The rotation of WHAT IS THE MOON matches the revolution, AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE). The stars AND PLANETS are POINTS in the night sky ON BALANCE. Great. “Mass”/ENERGY involves BALANCED inertia/INERTIAL RESISTANCE consistent WITH/AS what is BALANCED electromagnetic/gravitational force/ENERGY, AS gravity/acceleration involves BALANCED inertia/INERTIAL RESISTANCE (ON BALANCE); AS GRAVITATIONAL force/ENERGY IS proportional to (or BALANCED with/as) inertia/INERTIAL RESISTANCE; AS ELECTROMAGNETISM/energy is CLEARLY AND NECESSARILY proven to be gravity (ON/IN BALANCE); AS TIME is NECESSARILY possible/potential AND actual ON/IN BALANCE !!! GREAT.
By Frank Martin DiMeglio
This is a much better lecture than the one I had on classical mechanics in college. Thank you!
OMG I finally figure out the two body problem,thank you sooooo much.your video is always very logical and understandable. I’m so glad to find your channel.
One of the best videos that I found about using in non trivial way Lagrange mechanics with great python animation at the end
Glad you liked it!
Underrated as hell
The explanation is crystal clear.
thank you for the video
Thank you soooo much for this. I was looking for a thorough explanation for this, as I'm 13 and working on the iPHO.
great video as always. its also a scare free introduction to simulation
I think this is a great video....things like reduced mass need to be explained instead of all the hand-waving textbooks want to do.
The best explanatory physics video I have seen online. I wish I was your student.
oh, how nice. thanks!
Outstanding Job.
Thanks for a great video. I've learned so much from this, it's amazing. Please make more videos like this.
This video is so underrated...
thank you!
This is an amazing video. I think this derivation was probably outside the scope of what I was looking for but I got so excited at the end when you got the orbits to work and created that effective potential plot. I definitely want to try this in my free time. Using the numerical method you used, would it be possible to do something similar to this for 3 bodies or more and how hard would to show the orbits on screen, if not all the bodies are in the same orbital plane?
the 3-body problem cannot be currently solved
@@lulwahabduljabbar You can't analytically but you can numerically. I did it using the Runge-Kutta method not to long ago but that isn't the best numerical method for something like this.
Thank you so much! It was really helpful
At 8:46 are you not missing m2Rdot^2 ?
yeah but in the next step he does add it
To add to my comment about elliptical orbits. The Lagrangian T=T-U=1/2MR'*2+1/2^r'*2-U(r) when you assume R's velocity is constant it oversimplifies and ignores the acceleration I want to isolate. If r vector is oscillating with a sin wave acceleration the center of mass has to be oscillating with m/M*sin wave acceleration. The system is going to get the potential to a minimum. This is the mechanism that induces entropy. We need to add a component that equates the loss of acceleration in the bodies with the loss of change in potential energy. This is a very important fundamental mechanism of energy. If we solve for the acceleration of R can you, we isolate a clean answer.
Love it
Thanks for the great uploads
Glad you enjoy it!
I'm from India,
One of the best video, Sir
Thank you so much, it's really helpful, make more video's like this,
Thank you Sir
muy buen video, me ayudo muchísimo para la facultad :)
saludos desde argentina
at 42:52 there must be a wrong formula for F2 - when we divide norm(r) by mag(r)**2 this is no longer inverse square law. That norm(r) seems inappropriate because as far as i know it does the same as mag(r).
I have been working on a derivation of the acceleration on the center of mass that you hold to zero in order to constrain the system. In an elliptical orbit the gravitational force and centrifugal force are out of balance and the imbalance is in one direction. The force exerted on the center of mass is not zero. Some of the acceleration in the orbiting body must be transferred to the orbited body, conservation of energy requires it. This would mean an elliptical orbit slowly accelerates the whole system and forms a stable circular orbit given sufficient time. This is the mechanism that keeps the solar system intact. At the point you apply the Lagrange, instead of holding the acceleration of the center of mass to zero how about isolating the acceleration in the large mass. I have what I think is the answer 1/2ma=MA, a is the acceleration added to a circular orbit to induce an elliptical orbit. 1/2 comes from the final stable circular orbit being the mean velocity between the two orbits.
This makes the formation of the solar system completely different. this is also the basis I will propose a unified theory. Give me a clean derivation and we could win a Nobel.
Rip L Martin
Great video. Thank you! But why can we solve an open integer without getting a constant? 26:23
At 11:25, you mention that the potential energy function U(r) only takes in "r" as in the relative position between the two masses, and not R as the position of the center of mass. Why does the potential energy only depend on the relative location between the two bodies? Thank you :)
When you wrote the Lagrangian, is r the distance the objects are from each other? Also, may this discussion extend to (classical) scattering? Also, do you have another video that explains why certain objects are in orbits (whether periodic or not) while some objects collide? I’m finding these mechanics to be difficult.
What is the physical interpretation of the minimum in the potential plot? Does it imply that the net force is 0? Because the derivative of the potential wrt r should be 0 for a critical point (aka the net force). So does that imply that F_centrifugal = F_real?
The minimum would be where you would get stable circular orbits
amazing video
Thanks!
At 23:34 time stamp, why is it that the partial of L w.r.t theta dot is the angular momentum? is there any physical reason?
It's been a while since I looked at this, so here are two answers that might not be the best.
1) In Lagrangian mechanics, if you have a generalized coordinate (q_i), then the partial of L wrt to q-dot is the generalized momentum. In this case, we just call that the angular momentum
2) In general, we know that the partial of L wrt theta-dot is a constant. We can just pick that constant to be l and the units work out as angular momentum
@@DotPhysics
Thanks, that clears things up! I had another small question. At 23:35, when you take the partial of the Lagrangian with respect to theta, you equate it to 0. I know this is because you assume every variable is constant but isn't theta dot dependent on theta? So differentiating with respect to theta should not imply that theta dot is 0 right? Its like differentiating a velocity function with respect to position, it wouldn't be 0(?) My knowledge in multivariable calc is limited thats why this question may seem strange but hope u can help me through that.
Can we arrive at the ellipse from the potential differential equation?
Thanks.
how do you know that the potential does not depend on R?
Ok, I've spent two days straight on this, and I still don't get it. How am I supposed to "update the momentum" that you say to do at 28 minutes.
If I just want to do a 'simple' upwards ball throw from Earth at the speed of say 10km/s, without any angles or atmosphere, and with the mass of the ball irrelevant for the center mass, I have arrived that my starting equation is:
10,000x-((6.67*10^-11)*(5.97*10^24)/((6.37*10^6+distance traveled(0))^2)0.5x^2=10,000x-4.9x^2, which is a basic parabola.
And in order to find out where the ball is in ten minutes, I can certainly manually subtract x=1 from 10,000, plug the result into the distance, and repeat the whole process six hundred times, but I understand calculus was designed to help with that? The links to the equations provided don't work (Ug is not defined At or near line 37: U=Ug+Uc) and (v1cirle is not defined At or near line 17: star1.v=vector(0,v1cirle,0)) and I wouldn't know how to code anyway.
Any explanations I can find online either assume the gravity remains constant, try to complicate the problem with a bunch of stuff like the rocket exhaust, talk about vectors, or just kinda... assume I guess that I'd know how to update the momentum. And maybe if I went though the whole calculus curriculum again I'd find it obvious, but I really don't.
I would appreciate the help.
Absolutely fantastic presentation. This channel is a real gem. I wish "The Algorithm" had suggested it sooner!
thank you very much! Glad you liked it.
Who knew the harmonic mean of two masses would show up there?
Why do we need to solve the Euler-Lagrange equation for both r and theta?
You always solve the EL equations for all of your generalized coordinates to retrieve the equations of motion. In this case, the generalized coordinates are r and theta
mmmm...i like boxes. I use clouds personally but boxes are just as tasty.
great sir you are a genius and brillant tnx
I'm just a mere mortal - and I've spent A WHOLE BUNCH of time working on physics (like 30 years).
Dope 🎉
to everyone revising for the finals, good luck! 😭
Is this undergraduate year 1 physics?
This would be for upper level undergraduate physics. I cover this in the first or second semester of Classical Mechanics.
@@DotPhysics ah, so I won't be facing this shit in year 1 physics
@@jarjuicemachine lol, just confirming
niceeee
18:48 are called minors
@ 1:11 HERE'S MY PROBLEM: don't show a 2D x,y-plan if you want to describe a 3D situation. It is not even the plane in which these objects orbit!
@ 4:25 It's nothing but the dot-product of the two r-dot vectors. He doesn't explain it too ... despite all his talking. I give up here. Bye.
7:51 when I pause the video, it is miserable, that the TH-cam overlay appears and blocks the important reading of the formula! I need the pause to let the formula "sit in"!!
is there any option to turn overlay off/on, when I want?
Also the TH-cam-font, like so many others, are miserable/confusing: iI1lLoO0t | C()
the small l should have a "bent foot" while the small t doesn't need it, as long as it is clearly distinguisable from + !!!
Other fonts play around with unnecesssary serifes, whilst still not resolving the unambiguity problem.