Summary: Mechanics problem related with Calculus (differential equations)
Hi everyone, I would like some help in that task, if anyone would be willing to help :) Namely I have a problem from particle dynamics. "D:" means given info... so, D: m,g,h,b, miu. We're looking for v0 and S as given...
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Above is the figure of the problem.
I am trying to solve x(t) and differentiate it to obtain v(t); however, I have difficulty solving the differential equation shown below.
$$ v(t)=\int a(t)dt=\int \frac{B(\varepsilon-Blv)d}{Rm}dt \Rightarrow \frac{dx}{dt}=\frac{B\varepsilon...
1. Homework Statement
2. Homework Equations
euler
##e^{ix} = cos(x) + i*sin(x)##
##e^{-ix} = cos(x) - i*sin(x)##
3. The Attempt at a Solution
I'm starting with differential equations and I'm trying to understand this solution including complex numbers:
First we determine the zeros. I...
1. Homework Statement
2. Homework Equations
$$F = \nabla \phi$$
3. The Attempt at a Solution
Let's focus on determining why this vector field is conservative. The answer is the following:
I get everything till it starts playing with the constant of integration once the...
1. Homework Statement
x(dy/dx) = 3y +x4cos(x), y(2pi)=0
2. Homework Equations
N/A
3. The Attempt at a Solution
I've tried a couple different ways to make this separable, but you always carry over a 1/dx or 1/dy term and I can never fully separate this. I've also tried to do a Bernoulli...
I am trying to determine an outer boundary condition for the following PDE at ##r=r_m##: $$ \frac{\sigma_I}{r} \frac{\partial}{\partial r} \left(r \frac{\partial z(r,t)}{\partial r} \right)=\rho_D gz(r,t)-p(r,t)-4 \mu_T \frac{\partial^2z(r,t)}{\partial r^2} \frac{\partial z(r,t)}{\partial t} $$...
Hey all,
I hope this is the correct forum section to post this in.
I heard about this problem from a youtube video but I've not been able to simulate it because the video was meant only for an introduction into PID control.
Here's the problem:
A remote control helicopter is hovering just...
1. Homework Statement
Find Orthogonal Trajectories of ##\frac{x^2}{a}-\frac{y^2}{a-1}=1##
Hint
Substitute a new independent variable w
##x^2=w##
and an new dependent variable z
##y^2=z##
2. Homework Equations
3. The Attempt at a Solution
substituting ##x## and ##y## I get...
1. Homework Statement
2. Homework Equations
3. The Attempt at a Solution
Could you tell me is there something specific that I need to the with sin(xy)? Thanks
Hi!
When we want to look at different singular points for e.g Bessel's eq. $$u´´(x) + \frac{u'(x)}{x} + (1- \frac{n^2}{x^2})u(x)$$.
We usually evaluate the equation letting x= 1/z. But I don't algebraically see how such a substitution ends up with $$w´´(z) +( \frac{2}{z}-...
Hey all,
I don't understand what makes a differential equation (DE) linear.
I found this: "x y' = 1 is non-linear because y' is not multiplied by a constant"
but then also this: "x' + (t^2)x = 0 is linear in x".
t^2 also isn't a constant.
So why is this equation linear?
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COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
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COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
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COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
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COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
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COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081
COPYRIGHT strictly reserved to A. K. Nandakumaran, P. S. Datti & Raju K. George, Department of Mathematics, IISc Bangalore. Duplication PROHIBITED.
Lectures: http://www.nptel.ac.in/courses/111108081/
Syllabus: http://www.nptel.ac.in/syllabus/syllabus.php?subjectId=111108081