What is Time derivative: Definition and 63 Discussions
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable denoting time is usually written as
I'm having a hard time understanding some concepts and would really appreciate some help(not super smart so I need some things basically dumbed down). In my physics lab we're going over Newton's Second Law. There's a statement in the lab papers I don't understand. It states "As you should know...
I am completely stuck on problem 2.45 of Blennow's book Mathematical Models for Physics and Engineering. @Orodruin It says
"We just stated that the moment of inertia tensor ##I_{ij}## satisfies the relation$${\dot{I}}_{ij}\omega_j=\varepsilon_{ijk}\omega_jI_{kl}\omega_l$$Show that this relation...
Lets consider T(\vec{p})=\frac{\vec{p}^2}{2m}=\frac{\vec{p}\cdot \vec{p}}{2m}. Then \frac{dT}{dt}=\vec{v}\cdot \vec{F}.
And if we consider
T=\frac{p^2}{2m} than \frac{dT}{dt}=\frac{1}{2m}2p\frac{dp}{dt}
Could I see from that somehow that this is \vec{v}\cdot \vec{F}?
Hi Guys
Sorry for the rudimentary post. I am busy with a numerical solution to a mechanics problem, and the results are just not as expected. I am re-checking the mathematics to ensure that all is in order in doing so I am second guessing a few things
Referring to the attached scan, is the...
I am trying to find the equations of motion of the angular momentum ##\boldsymbol L## for a system consisting of a particle of mass ##m## and magnetic moment ##\boldsymbol{\mu} \equiv \gamma \boldsymbol{L}## in a magnetic field ##\boldsymbol B##. The Hamiltonian of the system is therefore...
I'm not sure about my proof. So please check my step. I used log as a natural log(ln).
Specially, I'm not sure about "d/dt=dρ/dt d/dρ=i/ħ [ρ, H] d/dρ" in the second line. and matrix can differentiate the other matrix? (d/dρ (dρ lnρ))
Let us suppose we have a functional of f such that ##f=f((\vec{r}(t),t)## where ##\vec{r}(t) = a(t)\vec{x}(t)##.
I am trying to derive an equation such that
$$\left.\frac{\partial}{\partial t}\right|_r = \left.\frac{\partial }{\partial t}\right|_x + \left.\frac{\partial \vec{x}}{\partial...
I'm having a hard time understanding how exactly to evaluate the expression}
$$\partial_t \mathcal{T}\exp\left(-i S(t)\right)\quad \text{where}\quad S(t)\equiv\int_{t_0}^tdu \,H(u) .$$
The confusing part for me is that if we can consider the following:
$$\partial_t \mathcal{T}\exp\left(-i...
So I just wanted to see if anyone could offer some suggestions. So in my mind this seems impossible, in the case of electric field a jump in time derivative of that field would indicated in my mind that electric charge was either introduced or removed from the system instantaneously which would...
Hi, just a question regarding neumann conditions, I seem to have forgotten these things already. I think this question is answerable by a yes or a no.
So given the 2D heat equation,
If I assign a neumann condition at say, x = 0;
Does it still follow that at the derivative of t, the...
here I am trying to find ##\frac{d}{dt}dx## where ##x(t)## is the position vector
Now ##\frac{d}{dt}(v_x(x,y,z,t)dt)=\frac{dv_x}{dt}dt=\frac{\partial v_x}{\partial t}dt+\frac{\partial v_x}{\partial x}dx+\frac{\partial v_x}{\partial y}dy+\frac{\partial v_x}{\partial z}dz##
Now dividing by ##dx##...
I have been reading a book on classical theoretical physics and it claims:
--------------
If a Lagrange function depends on a continuous parameter ##\lambda##, then also the generalized momentum ##p_i = \frac{\partial L}{\partial\dot{q}_i}## depends on ##\lambda##, also the velocity...
Homework Statement
I want to prove that ##\frac{\partial \langle x \rangle}{\partial t} = \frac{\langle p_x \rangle}{m}##.
Homework Equations
$$i\hbar \frac{\partial \Psi}{\partial t} = -\frac{\hbar^2}{2m} \frac{\partial^2 \Psi}{\partial x^2} + V \Psi$$
The Attempt at a Solution
[/B]
So...
Homework Statement
We have the equation for gravity due to the acceleration a = -GM/r2, calculate velocity and position dependent on time and show that v/x = √2GM/r03⋅(r/r0-1)
Homework Equations
x(t = 0) = x0 and v(t = 0) = 0
The Attempt at a Solution
v = -GM∫1/r2 dt
v = dr/dt
v2 = -GM∫1/r2...
Homework Statement
Show that for a second order cartesian tensor A, assumed invertible and dependent on t, the following holds:
## \frac{d}{dt} det(A) = det(a) Tr(A^{-1}\frac{dA}{dt}) ##
Homework Equations
## det(a) = \frac{1}{6} \epsilon_{ijk} \epsilon_{lmn} A_{il}A_{jm}A_{kn} ##
The...
Homework Statement
Problem 1.7 in Griffiths "Quantum Mechanics" asks to prove
$$\frac{d\left \langle p \right \rangle}{dt}=\left \langle -\frac{\partial V}{\partial x} \right \rangle$$
Homework Equations
Schrödinger equation
The Attempt at a Solution
I was able to arrive at the correct...
If energy is ihw and p is ihk, can force be written as derivatives of these? Might the fundamental forces just be some patterned change in the change of the wave functions of Dirac's equation?
Edit: the title should be "Time derivative of ihk" but I can't edit the title.
An inductor and resistor are arranged in parallel to a constant voltage source. There is a switch connected to a terminal on the inductor that can create a closed loop that includes either the voltage source, or the resistor. The switch is left connecting the source and inductor for a long...
Homework Statement
## \frac{d}{dt}\gamma(t)\vec{u(t)} ##
Homework Equations
See above
The Attempt at a Solution
This comes from trying to verify a claim in Chapter 12 of Griffiths Electrodynamics, 4th. edition (specifically Eq. 12.62 -> Eq. 12.63, if anyone has it on hand).
I would have...
Quick question (a little rusty on this): Why don't unit vectors in Cartesian Coordinates not change with time? For example, suppose \mathbf{r} (t) = x(t) \mathbf{x} + y(t) \mathbf{y} + z(t) \mathbf{z} How exactly do we know that the unit vectors don't change with time?
Or in other words...
Just using basic dimensional analysis, it appears the time derivative of centripetal acceleration is ## \vec{r} \omega^3 ##, but this intuitive guess would also extend to higher order time derivatives, no? Implying:
## \frac {d^n \vec{r}}{dt^n} = \vec{r} \omega^n ##
It seems to follow from the...
I was trying to compute the time derivative of the following expression:
\mathbf{p_k} = \sum_i e_{ki}\sum_{n=0}^{\infty} \frac{(-1)^n}{(n+1)!} \mathbf{r_{ki}}(\mathbf{r_{ki}\cdot \nabla})^n \delta(\mathbf{R_k}-\mathbf{R})
I am following deGroot in his Foundations of Electrodynamics. He says...
When we obtain the velocity vector for position vector (r, θ, φ)
Why do we take the time derivative of the radial part in the 3D Spherical Coordinate system only?
Don't we need to consider the polar angle and azimuthal angle part like (dr/dt, dθ/dt, dφ/dt)?
Homework Statement
For the equation ∇ x E = -∂B/∂t I took the curl of both sides to get
∇ x (∇ x E) = ∇ x -∂B/∂t
I feel like it'd be very wrong to pull out the time derivative. Am I correct?
Homework Statement
Solve ∂v/∂θ and ∂v/∂r. (refer to attached image for equations)
Homework Equations
Refer to attached image. note that the velocity is expressed in cylindrical coordinates and attention must be paid to the directional unit vectors eθ and eρ.[/B]
The Attempt at a Solution...
Is the time derivative of a curl commutative? I think I may have answered this question... Only the partial time derivative of a curl is commutative? The total time derivative is not, since for example in cartesian coordinates, x,y,and z can themselves be functions of time. In spherical and...
Homework Statement
So the first part asks to prove the time derivative of kinetic energy is dT/dt=F dot product v which I did not problem. but then the second part of the problem asks to prove that if the mass is changing with time then the time derivative of d(mT)/dt=F dot product m and I'm...
In chapter 1 of the book "Introduction to Mechanics" by Kleppner and Kolenkow, the derivative of a generic vector ##\vec{A}## is discussed in terms of decomposing an increment in ##\vec{A}##, ##Δ\vec{A}##, into two perpendicular vector vectors; one parallel to ##\vec{A}## and the other...
Homework Statement
I have somewhat general question about time derivative of a vector.
If we have
r=at2+b3
it's easy to find instantaneous acceleration and velocity(derivative with respect to dt)
v=2at+3bt2
a=2a+6bt
But consider this position vector
r=b(at-t2)
where b is constant vector and a...
What would be some important properties of a universe where Force = Mass * Jerk and objects stay in constant acceleration until acted upon by a net force? (if we ignore the fact that objects would reach the speed of light, and just deal with classical mechanics)
Is rather a question of calculus skills, but how do I get the time derivative of the Hubble parameter here in [1]? Is it the Leibnitz rule, the chain rule, some clever re-arrangement?
thank you
Typically in mathematics time derivative is linear in the sense that constants are pulled out the operator which then operates on a time dependent function. But in quantum mechanics we say linear to mean that the operator passes over the coefficients of the kets (which themselves might be time...
Hey guys,
So I'm reading something about vector potentials and I've come across this one line which is really annyoing me. Here's how it goes
\frac{d}{dt}\mathbf{A}=\frac{\partial \mathbf{A}}{\partial t}+\frac{\partial \mathbf{r}}{\partial t}\cdot \frac{\partial }{\partial...
Let \gamma^{\rho} \in M_{4}(\mathbb{R}) be the Majorana representation of the Dirac algebra (in spacetime signature \eta_{00} = -1), and consider the Majorana Lagrangian \mathcal{L} = \mathrm{i} \theta^{\mathrm{T}} \gamma^{0} (\gamma^{\rho} \partial_{\rho} - m) \theta, where \theta is a...
Hi All,
I have a problem in understanding the concept of dirac delta function. Let say I have a function, q(r,z,t) and its defined as q(r,z,t)= δ(t)Q(r,z), where δ(t) is dirac delta function and Q(r,z) is just the spatial distribution.
My question are:
1. How can I find the time derivative...
On page 13 in Landau-Lifgarbagez Mechanics, the total time time derivative of the Lagrangian of a closed system is given to be,
\frac{d L}{d t} = \sum_i \frac{\partial L}{\partial q_i} \dot{q_i} + \sum_i \frac{\partial L}{\partial \dot{q_i}} \ddot{q_i}
Why does this stop here? I mean, why...
According to my book:
\frac{d}{dt} \langle Q \rangle = \frac{i}{\hbar} \langle [\hat{H}, \hat{Q}] \rangle + \langle \frac{\partial \hat{Q}}{\partial t} \rangle .
No derivation for this is given. How can derive you this?
Homework Statement
Finding the time derivative of sin^2( \alpha ), knowing that \dot \alpha ≠ 0
Homework Equations
i know that \frac {d}{dt} sin ( \alpha ) = \dot \alpha cos ( \alpha)
The Attempt at a Solution
That should give
\dot \alpha ^2 cos^2( \alpha )
But it's...
I am curious if there are any issue with commuting the curl of a vector with the partial time derivative?
For example if we take Faraday's law:
Curl(E)-dB/dt=0
And I take the curl of both sides:
Curl(Curl(E))-Curl(dB/dt)=0
Is
Curl(dB/dt)=d/dt(Curl(B))
I assume this is only...
Trying to teach myself physics and I've run into a problem I don't quite understand.
"The magnitude of dA/dt can be found by the following geometrical argument. The change of A in the time interval t to Δt is"
ΔA = A(t + Δt) - A(t)
And then somehow it gets to
|ΔA| =...
Why is the TDSE first derivative in time. Now I know that it is required so that the wave functions are complex... but is there any physical interpretation for this requirment??
Given an operator Q, how do we derive the relationship
\frac{dQ}{dt}=i\left[H,Q \right]+\frac{\partial Q}{\partial t}
?
I had thought that this was only true in the Heisenberg picture. But Greiner has it here (eq 8.19) for an operator in the Schrodinger picture.
No need to show...
On the Wikipedia page for http://en.wikipedia.org/wiki/Heisenberg_picture#Mathematical_details" we find this relation
\frac{d}{dt}A(t)=\frac{i}{\hbar}[H,A(t)]+\left(\frac{\partial A}{\partial t}\right)
I don't understand what the distinction between
\frac{d}{dt}A(t) and...
Hi all, I ran into a bit of an issue trying to figure out how to properly differentiate the magnetic force due to particle interactions. To be specific, I'm actually looking for the time derivative of acceleration (jerk) due to the magnetic force, but it's essentially the same problem.
For...
Homework Statement
Electromagnetic radiation is emitted by accelerating charges. The rate at which energy is emitted from an accelerating charge that has charge q and acceleration a is given by:
\frac{dE}{dt} = \frac{q^{2}a^{2}}{6\pi\epsilon_{0}c^{3}}
where c is the speed of light...
Hello,
I am trying to learn about some basic quantum mechanics.
http://farside.ph.utexas.edu/teaching/qmech/lectures/node35.html this website shows that the time derivative of the momentum expectation d<p>/dt = -<dV/dx>
The part that i am not getting is how the writer goes from the...
I'm wondering, how does 2 multiplied by the first and second time derivatives of x equal the time derivative of the time derivative of x squared. Thanks.