System Definition and 1000 Threads

Hello! I am reading "A First Course in General Relativity" by Schutz and in chapter 8 (second edition) he introduces Nearly Lorentz coordinate system. He says that we can always find some coordinates such that the metric is: $$g_{\alpha\beta}=\eta_{\alpha\beta}+h_{\alpha\beta}$$ with...

Some time ago I made a modelling project and obtained a plot. Now, I want to remember what the transfer function was, as I want to try changing the parameters. The graph is the following: How can I obtain the transfer function? Thanks a lot

If I have a single spin 1/2 particle, I know that it's total spin in any direction with unit vector can be computed by using the operator σ•n where σ_i are the pauli matrices. Suppose however I had a multiparticle system, is there a generalization of the pauli matrices (which let's call ρ_i) so...

Homework Statement Imagine exactly same two bodies (same mass, same surface/friction etc) are attached with a string/spring and they suddenly start pulling towards each other with equal force. I can imagine they will move towards the center. If there is a chain (with defined number; not...

Homework Statement So imagine 4 rigid rods connected together to form a dashed quadrilateral as shown in the picture. Now AB is fixed, can not be changed in anyway, while all other sides (AD, BC and CD) are connected but can move freely. The initial conditions (dashed quadrilateral) are given...

Homework Statement A circular ring (2m, R) with a small insect of mass m on its periphery, is placed upon smooth horizontal surface (axis of rotation passing through center and perpendicular to the ground i.e disk is lying horizontally) . The insect starts moving with velocity v w.r.t ground...

Homework Statement There are 2 situations- 1)a rod of length L is lying on a smooth horizontal surface with its one end hinged to the ground, a ball traveling with a velocity v hits its other end and comes to rest, How is the net external torque about hinge point O zero? 2) in the second case...

1. The problem statement, all variables and given/known dana I was revisiting University physics textbook and came across this problem. We learned new coordinate systems in classical mechanics classes so I wanted to see if I can apply this to the problem of force on semicircular part of the...

Homework Statement Solve the following system of equations Homework Equations A1 + A3 = 0 cA1 + A2 + A4 = 0 dA1 + cA2 + w^2 A3 = 1 dA2 + w^2A4 = 0 The Attempt at a Solution https://imgur.com/YSG5oGN - Page 1 https://imgur.com/dGbccsE - Page 2

Does anybody know of inexpensive MODBUS devices that we can purchase for some medium-scale compatibility testing with a new controller that we are building? There are some moderately expensive products from Schneider Electric, but we're hoping to find some more "jellybean" products that we can...

When in history did our reward system develop, in order to ensure human reproduction? And what drives lower animals to reproduce? Instinct The reward is the survival of the lineage. but do animals know this as well? Do they have some kind of consciousness that they (well, actually not them...

Hey! :o Is the system $$x^3+y^3+z^3=1 \\ x\cdot y\cdot z=-1$$ in a region of the point $(1; 1; 1)$ uniquely solvable for $y = y (x) $ and $z = z (x)$ ? How can we check that? Could you give me a hint? (Wondering)

Homework Statement Three slim rods with the same length L are placed in a inverted U shape, as the figure shows. The masses of the vertical rods are the same, while the third bar has the mass 3 times bigger than the first or the second rod. The rods' thickness should be ignored. Find the moment...

Hey guys, I would appreciate some help with the math behind creating a working coordinate system for a robotic arm. I am currently trying to determine what servo angles are necessary to align a robotic arm's claw to the given coordinates. Geometrically simplified, the robotic arm is a...

Homework Statement Hello, this is like an experiment of engineering.It is called a induction stove. The system consists of a bycicle, where I am going to pedal. This will turn a disk that have 20 small magnets around its circuference. Once the disk starts to turn, it will produce a constant...

Hi to all! My question is: Does the relative position of the barycenter of the Earth-Moon system change due to mass distribution changes in the system and would this affect the Earth-Moon distance? For example: Could the sea level rise change the Earth-Moon distance? The only formula I found...

> Operator $$\hat{A}$$ has two normalized eigenstates $$\psi_1,\psi_2$$ with > eigenvalues $$\alpha_1,\alpha_2$$. Operator $$\hat{B}$$ has also two > normalized eigenstates $$\phi_1,\phi_2$$ with eigenvalues > $$\beta_1,\beta_2$$. Eigenstates satisfy: > $$\psi_1=(\phi_1+2\phi_2)/\sqrt{5}$$ >...

Hi, I was trying to solve the simplest problem of planetary motion (for one planet). The equations should be: ##F_x = m \frac {d^2x} {dt^2} = G \frac {Mmx} {r^3}## ##F_y = m \frac {d^2y} {dt^2} = G \frac {Mmy} {r^3}## where ## r = \sqrt{x^2 + y^2}## So I re-wrote the system like this...

Ignoring special relativity theory，maxwell equation are deduced in which coordinate system?In most electrodynamics textbook,maxwell equation are deduced without specifying which coordinate we are using.For example,when we are solving poisson equation in static case，it seems we can freely choose...

Homework Statement How does Hodgkin's lymphoma effect the "normal" function of the lymphatic system? Homework Equations N/A The Attempt at a Solution After research I have found out that HL casues lymph nodes to become inflames. I have concluded HL causes lymph fluid to get blocked at lymph...

Homework Statement I need to find the discrete time equivalent of the following system: \begin{bmatrix} \ddot{x} \\ \dot{x} \\ \ddot{\theta} \\ \dot{\theta} \end{bmatrix} = \begin{bmatrix} 0 & 0 & 0 & 4.2042857 \\ 1 & 0 & 0 & 0 \\ 0 & 0 & 0 & 105.1071428 \\ 0 & 0 & 1 & 0 \end{bmatrix}...

Hello, Can you tell me please the glucose physiology in respect to the lymphatic system in short? Is there glucose inside the lymph? How does glucose enter/leaves the lymph? Are the glucose levels in blood related to the glucose levels in lymph? thanks!

I have a problem where I want to find out the static pressure over a city in a water pipe system. As I know the elevations over the city I was first thinking of just using p = rho * g * h, but this should only apply if the pipe system were under water (if I use the density of water at least). So...

I tried to convert the second order ordinary differential equation to a system of first order differential equations and to write it in a matrix form. I took it from the book by LM Hocking on (Optimal control). What did I do wrong in this attachment because mine differs from the book?. I've...

Hi. Usually, Computer Programmers use Flow Charts, Algorithms, or UML diagrams to build a great software or system. In the same manner, in Mathematics, what do Mathematicians use to build a great system that they want to build. Category Theory is at the highest level of abstraction; then...

Homework Statement Under the action of force P the constant acceleration of B is 6 m/s^2 up the incline as in figure. For the instant when B's velocity is 3 m/s up incline, what is the velocity of point C? How do I solve this using constraints? [/B] Homework Equations For a pulley system ΣT.v...

Homework Statement A carriage is mounted on a spring, as shown in the diagram. The bottom of the spring is fixed to the ground. The carriage (loaded with its passenger) has a mass of 150kg. The carriage can only move vertically. The natural length of the spring is 10m and its spring...

Homework Statement : A block B of mass m is suspended from a cord of length l attached to cart A of mass M as shown in the figure. The horizontal surface on which the cart moves is smooth. Initially the cart and the block are at rest in the position shown. Now the block is released. Take M=2kg...

Homework Statement Homework EquationsThe Attempt at a Solution I've resolved all the relevant forces (tension, weight, normal force), but upon looking at the mark scheme, there is no normal force to be resolved. Forgive me if I'm missing out on something obvious, but shouldn't there be a...

It's really confusing if the frictional force IS an external force.. My guess is the frictional force isn't an external force and therefore I can observe the momentum conservation even with friction if I carefully measure the velocity right before and after the collision. But I'm not sure about it..

Homework Statement Im going over some revision for fibre optics and I've come across an example question to calculate the power margin of the system with the following info is given: transmitter power = -10dBm Connector loss = 1.5dB Attenuation = 3dB/Km Total length= 2KM Receiver threshold =...

Hello, I've been told that 'natural units' ensure ##\hbar=G=c=\mu_0=1## but... when I look for it in Wikipedia I find that there are (mainly) two kinds of natural/geometrized units: The Planck ones and the Stoney ones, (https://en.wikipedia.org/wiki/Geometrized_unit_system) Also, some...

Homework Statement If a system comprised only of two electrons was physically possible (such as positronium but with two electrons), what would its energy levels be and how would they relate to the energy levels of Helium? Homework Equations ##E_{Helium} = E_{n1}+E_{n2}=-\frac{\mu Z^2...

Homework Statement for this question i think the sludge age is wrong. Homework EquationsThe Attempt at a Solution Based on the formula given , The suspended solid in effulent should be = (Q-Qw) , which is 8100-150= 7950 , am i right ? Correct me if i am wrong ... Or the 8100 m3/s given is the...

Homework Statement Given a system with a Lagrangian ##L(q,\dot{q})## and Hamiltonian ##H=H(q,p)## and that the Lagrangian is invariant under the transformation ##q \rightarrow q+ K(q) ## find the generating function, G. Homework EquationsThe Attempt at a Solution ##\delta q = \{ q,G \} =...

Homework Statement Homework Equations n/a The Attempt at a Solution I am going through the final exam problem sets right now and just looked at the answer key and wondering where in this system there could be thermal energy? while i was working through the problem i assumed no thermal energy...

If I move a coordinate system by an angle theta, why does the vector still have the same direction, but the components are different?

Homework Statement Consider a system of two quantum particles. Each particle has two quantum states, one with zero energy and one with energy ε>0. For each of the three cases, draw a table of the possible microstates α of the system, and find the canonical partition function Z(β). a)The two...

Homework Statement Two block M1 and M2 rest upon each other on an inclined plane. Coefficient of friction between surfaces are shown. If the angle θ is slowly increased, and M1<M2 then Options : 1- Block A slips first. 2- Block B slips first. 3- Both slip simultaneously. 4- Both remain at...

Homework Statement Homework EquationsThe Attempt at a Solution Work = W = ΔKE Case A: ΔKE = WTENSION - WSPRING - WGRAVITY Case B: ΔKE = WGRAVITY - WTENSION Case C: ΔKE - ΔPESPRING = WTENSION - WGRAVITY Case D: ΔKE + ΔPEGRAVITY = -WTENSION Case E: WSYSTEM = 0 Velocity and tension for...

(I hope this post doesn't cross the border into the forbidden realm of quackery and speculation.) I have what seems like a simple question about Special Relativity but I haven’t seen it discussed anywhere, nor has anyone I've asked. Does the nonlinearity of the Lorentz factor provide a way...

Suppose we have a quantum system ##Q## with an initial state ##\rho^{(Q)}##. The measurement process will involve two additional quantum systems: an apparatus system ##A## and an environment system ##E##. We suppose that the system ##Q## is initially prepared in the state ##\rho_{k}^{(Q)}## with...

I'm looking at what should be just a simple spring system where four identical springs are holding up a square, load-bearing pallet plate in a warehouse. Now, someone says the equation of motion for the vertical normal mode of vibration is simply d2z/dt2 = -4(k/m)z. Right away however, I see no...

Hi there guys, I was wondering does anyone have a layman's explanation of the GCRS as defined in the title. I am confused as to whether this is an inertial or non inertial system. In text modern reference books such as this (chapter 10, section 10.3.2) they define rotating/non rotating...

Homework Statement Solution: Homework Equations dp/dz = -ρh Pressure varies linearly with the depth. The Attempt at a Solution Firstly, I have calculated the pressure at point B. PB = PA - (0.3m)*(1000kg/m^3)*(9.81m/s^2) PB = 88057 Pa Calculating the pressure at point C. However, my...

Homework Statement Two spin ##\frac 12## particles form a composite system. Spin A is in the eigenstate ##s_z = + \frac 12## and Spin B is in the eigenstate ##s_x = + \frac 12## What is the probability that a measurement of the total spin will give the value ##0##? Homework Equations I know...

I need to explain to a student the meaning of number systems. I try to explain him that it is like a family of numbers that have some proprity. If one have an idea to expalin him the term, it will be helpful. I remind note about the term: A number system can be complex system number, rational...

Hi All. On Tuesday I have to present my research proposal for my undergrad research. I intend to model our solar system using general relativity and compare and contrast my results with observations. Attached is my paper that I had to submit to my adviser. He suggested that I talk about some...

Homework Statement The moment of inertia about an axis through the center of mass of a system consisting of two masses 3.0 and 5.0 kg connected by a rod of negligible mass 0.8m long is Homework Equations [/B] I = I1 + I2 The Attempt at a Solution I added all the moments of inertia of the...

Hello,Ive got a question and wondering if there is someone that could help me? I would really appreciate it! I am studying for an exam that I am going to have in a couple of weeks and it has been going great besides that I have been stuck on a question about tension in a preloaded system with a...