Questions tagged [mathematics]

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38 views

Lyaponuv stability condition of linear systems for homogenous P in V(x) = x^T P x

I am currently learning about using Lyaponuv functions to find Linear Matrix Inequalities (LMIs) as conditions for stability of a linear time invariant system. i.e. $$ \dot{x}(t) = Ax(t) $$ is stable ...
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58 views

Can you offer real-world examples of logarithm use? [closed]

Can you offer real-world examples of logarithm use? An example of a real-world layman application of logarithms is understanding amplifier power ratings. For example a 30 watt amp is not one third as ...
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1answer
51 views

How do rollercoaster designers calculate the ideal curve?

I've been looking into rollercoaster track designs and wondered how they mathematically calculate the ideal curves to fit some specific layout without creating excessive Gs or other rider discomfort ...
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1answer
33 views

Resolving the forces into components [closed]

okay so I am really struggling to see how to resolve the Normal reaction force and Weight into the r and theta direction please? Why is it that the angle is taken to the left of N and right of mg ...
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1answer
40 views

Question regarding the extreme wind velocity distribution in Eurocode

Above is the definition of the probability factor from Eurocode 1-4. It is used in context of calculating the extreme wind load on a building. Ignoring some other factors, it is used as follows: $$v_b ...
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1answer
48 views

FE Exam practice: “How many years until you're a millionaire?” [closed]

One of the early questions in the NCEES FE Industrial/Systems Exam studyguide has a solution that I can't decipher. The question is as follows: ...
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17 views

Scalability in the context of optimization and control systems

I am having a hard time trying to make sense of the phrase "Scalable optimization". I read from a few papers discussing that some global optimization solvers like BARON, ANTIGONE, etc. do ...
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1answer
88 views

Infinitesimal Strain Tensor in Cylindrical Coordinates

How can I obtain the below formulas of infinitesimal strain in cylindrical coordinates using matrix calculation given the first formula? I find it hard to study them because I still don't know how to ...
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1answer
50 views

Stretch in Infinitesimal strain theory

In the picture above we have the expression of stretch with respect to strain tensor, but in case of infinitesimal strain theory, we take stretch equal to 1+T.E.T I don't understand why by taking ...
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2answers
76 views

What's the name of the calculus used to make smooth transitions in roads?

So I'm not actually an engineer, I'm a novice computer programmer but I think in order to solve a problem I have I'm going to need some help from the world of engineering. I remember in high school ...
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1answer
55 views

Determine the parameters for this given nyquist plot

I have seen quite many of this type of question and I want to find how to solve them but I haven't cracked it yet. For example this is one: My thoughts so far: Replace $$s \rightarrow j\omega$$, $$G(...
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29 views

Could tic-mark labels on a graph have individual decimal digits with different signs?

I'm currently looking at a graph (figure 5 of Ede (1967), "Advances in Free Convection", in Hartnett and Irvine (eds.), Advances in Heat Transfer vol. 4, New York: Academic Press), in which ...
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3answers
76 views

Statically determinate system

The exercise is taken from linear algebra and its applications, prof. G. Strang Exercise 2.4.8 Truss I have already found that: m=n=8 → system is statically determinate, therefore solvable by ...
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1answer
60 views

Obtaining equation from real life

As I was studying about differential equation,then I got a question in my mind that we are taking out general solutions for a differential equation. Like for example - Q) $\frac{dy}{dx} = \left[\frac{...
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15 views

How to judge the character and sign of a dislocation?

I do understand that $ \mathbf b||\mathbf t$ for screw dislocation but I am unable to judge the sign of the dislocation. Again if $\mathbf b \perp \mathbf t$ how do I judge its sign? Any formula which ...
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44 views

Temperature Question

A thermistor, which has a Negative Temperature Coefficient (β) of 3300 (K) and a resistance ($R_o$) of $10\text{ k}\Omega$ at a reference temperature of 21ºC, is used to measure the temperature of an ...
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2answers
64 views

Is there any application of control engineering to the study of algorithms stability or computer science theory?

I am an undergraduate student in Electrical and Computer engineering. In our 5th semester we have a obligatory "Introduction to control systems course". I was wondering if these bunch of ...
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2answers
107 views

How to Derive the Differential Form of the Contintuity Equation

The book "Gas Turbine Engineering Handbook" by Boyce, on p. 117 states, the continuity equation, $ \dot m = \rho A V $, has as its differential form, $ 0 = \frac{d\rho}{\rho} + \frac{dA}{A} ...
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31 views

Are gas distribution networks tree-like?

I was wondering, if it is justified to say, that gas distribution network graphs (primarily in Europe) are typically tree-like. By gas distribution networks I mean municipal and regional distribution ...
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24 views

Finding characteristic time required to reach steady state in the pump equation

Consider the pump equation $$\rho \frac{\partial w}{\partial t} = K' + \frac{\mu}{r} \frac{\partial }{\partial r} \left(r \frac{\partial w}{\partial r} \right)$$ Subject to $w(r=R,t)=0$, $w(r=0,t)$ is ...
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1answer
79 views

How to calculate the torque for motors for a Core XY movment?

I am trying to design a simple setup that follows the core XY movement shown: I have been researching the statics behind this movement in order to calculate the minimum torque for the motor so I ...
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1answer
83 views

Does Finite Element Method use direct stiffness method?

Does Finite Element Method use direct stiffness method? Or it is another mathematical method? We definitely use direct stiffness method to solve frames. FEM is based on entirely this or depending on ...
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2answers
130 views

How high will a flywheel catapult launch a payload?

First off, this is not a homework question or anything like that. I'm trying to build a catapult to launch a payload using a flywheel as an energy device! It goes like this: The flywheel spins up to ...
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0answers
20 views

multidimensional function for object description

I want to simulate a bow tie antenna and build it up with a function. so far i have managed to create a piece of cake with sin and cos. Now I would like to expand the function and round off the ...
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26 views

how to obtain solution of this bessel equation using Frobenius method

Given this equation: $$ \frac{1}{r}\frac{d}{dr}\bigg(r \frac{dT}{dr} \bigg) - \bigg(\frac{2h}{bk} \bigg)(T-T_a) = 0 $$ I can let $x=r\sqrt{(2h/bk)}$ and $z=T-T_a$ to obtain the bessel equation using ...
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4answers
106 views

Swing safety: maximum load of beam (supported at one end, free with load on the other)

My husband and his dad built a fort for our two boys. Coming off of one side of the fort is a 4x6 wooden beam with a tire swing attached at the end. It is supported on one side by the fort, but not ...
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1answer
55 views

Is the identity matrix a tensor?

If we multiply the identity matrix by any vector or a matrix, then the result is the vector or the matrix themselves (like a mirror). Tensors represent physical quantities, so if it wasn't a physical ...
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24 views

RF Engineering - Cascading a 3 Port S-Parameter Network into a 4-Port S-Parameter network

I have been trying to cascade a 3-port scattering parameter network into a 4-port scattering parameter network that will ultimately be terminated by another 3-port network (as can be seen below). The ...
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1answer
42 views

Gaps in derivation of thermodynamic property equations

If $h=h(T, P)$. Does $ dh = c_pdT + \left[v - T\left(\frac{\partial v}{\partial T}\right)_P \right]dP \Rightarrow h_2 - h_1 = \int_{T_1}^{T_2} c_pdT + \int_{P_1}^{P_2}\left[v - T\left(\frac{\partial v}...
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0answers
36 views

How does NASA's QueSST X-59 jet work?

The QueSST (Quiet Supersonic Transport) is a project to create a more diffuse sonic boom in order to use supersonic flight commercially without the usual abrupt 1~2 psf pressure spike damaging the ...
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1answer
42 views

Calculating features of a 3 phase power timeseries

I have data from a number of high frequency data capture devices connected to generators on an electricity grid. These meters collect data in ~1 second "bursts" at ~1.25ms frequency, ie. ...
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0answers
28 views

Using complementary filter in rotation matrix

I am using accelerometer and gyroscope and try to compensate earth gravity. I figured out use of complementary filter, that calculates pitch and roll angle. On account of compensating gravity I am ...
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3answers
38 views

Placing an accelerometer on arbitrary position and define this as the new coordinate system

I'm working on a small home project and I'm looking to use an accelerometer for tilt sensing. I would like to be able to place it anywhere on the object. If I place it in a way that the coordinate ...
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1answer
24 views

How do I compute the torque in ft lbs to turn a screw and move a 2000 lb weight?

I am having trouble locating the calculations for finding the torque, in ft/lbs, required to turn a 1/2" screw with 13 threads per inch and pull 2000lbs 6 inches. .
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1answer
194 views

How can I implement S-curve motion profile on mobile robotic platform / wheeled robot?

I want to plan a robot's motion according to an S curve profile. I am following the article mention below, which contains basics related to S curve motion profiles in robotic platforms. https://www....
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30 views

Is a pyramid considered axisymmetric? Why so?

I read a source, I will not reference the source on this platform. They stated a pyramid is axisymmetric. Can you explain why if yes?
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1answer
246 views

Hansel-Spittel equation parameter determination

I am currently learning how to determine the Hansel-Spittel equation parameters. The equation has following form: $$\sigma= A \cdot e^{m_1\cdot T}\cdot(\epsilon^{m_2})\cdot \exp\left(\frac{m_4}{\...
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1answer
56 views

Air - rectangular membrane system vibration and natural frequency

I'm struggling with the following problem: The boundary conditions are $w(x,y) = 0$ around the edges. I am supposed to find the natural frequencies of the system as a whole, and find the solution ...
2
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1answer
106 views

Help understanding a control system represented by coefficients of theta?

I've been working with control systems and transfer functions recently, but I've come across a format that I haven't seen before using coefficients of theta, and I can't find any information about it. ...
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0answers
67 views

Converting nonlinear system into equivalent nonlinear of the Byrnes-Isidori normal form

I have a nonlinear system (Ball & Beam) which is described by the following equations of motion: $$ \ddot{y} + \frac{mg}{a} \sin(θ) -\frac{m}{a}y\dot{θ}^2 = 0 $$ $$ \ddot{θ} + \frac{2m}{b}y\dot{...
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19 views

Factoring in Efficiency in Equations

A pretty simple question, but one that's weirdly confusing me: I'm working with an equation for total water demand (Q) were w is the allowance for water wasted. w is typically 30%. Most books ...
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1answer
73 views

Input-output representation to state space

How do you create a state space representation of the following input/output equation: $$ \dot{y} = -ky + u + a\sin(ωt) $$ where the parameters $k$, $a$, and $ω$ are unknown. The end goal is to ...
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1answer
138 views

linearizing a non linear state space equation

I have this 1-DOF helicopter simulator. The motor's armature resistance is $R$, inductance $L$ and motor constant $K$ and reaction torque on the motor shaft is $τ$. $T$ is equal to $k_1w_2^2$ and $...
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0answers
63 views

Finding transformation of forces and moments

I have two sets of forces and moments, measured by two 6 DOF force/torque sensors at position A and B on a robot arm (B at end effector). My goal is to use this measurements to relate the forces/...
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0answers
44 views

Mathematical transformation of a heading angle to a roll angle

I'm trying to understand a function in a SIMULINK example of a path following UAV simulation. The gist is that, the UAV Waypoint Follower block provides a required heading from a list of waypoints and ...
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1answer
25 views

Are Loop Closure Equations and Holonomic Constraints the same thing?

I'm reading a book on robotics, and it has a different section on each term. The way both concepts are worded and phrased mathematically make them seem like they both constrain the configuration space ...
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1answer
40 views

Bounds to prove exponential stablity for given Lyapunov function

Problem 3.6 in Khalil's Nonlinear Control: Use given Lypunov candidate function to prove that the origin is exponentially stable. The system is $$\dot{x}=\begin{bmatrix}x_2\\-h(x_1)-2x_2\end{bmatrix},...
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1answer
37 views

How much energy do mass drivers need to project 1lb of material 1km/second

I am working on a geoengineering project that, at the moment, seeks to use many mass drivers to project lunar regolith (lunar soil) or other materials into space to create targeted shading effects on ...
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4answers
67 views

Planes, lines and distances: looking for engineering problems

In a week from now, I am going to teach a one-time class to first-year engineering students about 3D geometry, more specifically: distances between points and lines/planes, and the common ...
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1answer
90 views

How to obtain plant parametric model of given system?

Consider the system: $$ y(s)=b\frac{e^{−sτ}}{s+a}u(s) $$ where a,b are unknown, constant parameters and $\ τ>0 $ is an unknown delay constant. How can I obtain a plant parametric model for this ...