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Questions tagged [mathematics]

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19 views

What's the most anisotropic material? Is there a dense stiffness matrix?

The stiffness (aka. tangent modulus of the stress) can be represented as a symmetric 6-by-6 matrix, i.e. it has 21 independent components in the most general case. In the linear case, this matrix is ...
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3answers
50 views

Why do we get singularities in a solutions while modelling a physical systems?

I wonder why do we get some times singularities (position to be infinity or velocity to be infinity) in the solutions while modelling a real system and in spite of taking all real parameter values of ...
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11 views

Reformulate navier-stokes in terms of perturbation

I am reading this paper and trying to understand on page 14-15, First it rewrites Navier-Stokes in terms of a ''zero order problem'', and where $u_i = \mathscr{U}_i + u_i'$ , where $U_i$ is the base ...
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62 views

Help with Engineering Mathematics, Struggling to determine coefficients using methods detailed in this research paper

I am struggling with a curve fitting calculation below. the part I am stuck with is arguably the simplest part, which is determining the coefficients $\\K_3$ and $\\K_4$. It seems like it should be ...
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1answer
35 views

Question regarding calculation of angular velocity connected to coordinate transformation

So i need to calculate the angular velocity of the dark disk, $w^*_3$. In the master solution they state it is : $w^*_3 = w_3 + \overline{w_3}$ with : $w_3 = \frac{|\dot{r}|}{4a}$ $|\dot{r}| = v_a +...
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8 views

How to calculate new focal plane position when adding a lens to a lens system?

I am currently struggling with some lens equations. I hope this is the right place to ask such questions. What I'm trying to accomplish is to add a separate single lens to a camera setup and ...
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1answer
70 views

Changing fields from mathematics to control engineering [closed]

I did my undergraduate in maths and physics and will be working in control theory for my future job. Not to my surprise, my engineering background is rather lacking. I have taken a look at materials ...
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3answers
50 views

Calculate area of mesh?

I have expanded steel mesh that I use to make garden cages: I would like to know how much sunlight the mesh blocks. I think I need to calculate the area that the mesh takes up (per square inch) and ...
3
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3answers
152 views

Should Engineers Understand Equations without Relying on Derivations?

As I've progress through my undergraduate engineering program, I've noticed a shift away from physical intuition - understanding why certain phenomena or equations make sense because of basic patterns ...
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2answers
54 views

finding the center of rotation between 2 rigid bodies

I feel a little lost. I think my problem is quite simple, but unfortunately, my knowledge of math is also simple. I have two rigid bodies that move relative to each other. I know two points of each ...
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0answers
13 views

How to sample Mean-Time-To Failure values from a Weibull Distribution with shape 1.5?

I have a mean time to failure (MTTF) recorded from 100 systems which is 6.5 years. The shape parameter of my component is given with k = 1.3 (based on a list the from literature). Now I want to ...
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9 views

In which situations should I use function f(x)=-x or f(x)=1/x in multiple-criteria decision analysis (MCDA)

Is there any difference if someone uses function f(x)=-x or f(x)=1/x to minimize a criteria in a decision process supported by multicriteria analysis? If it does, in which situations should I use one ...
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1answer
35 views

Help with determining the dimension change in the xyz direction of a component under a load?

I'm stuck on this question. I got the first part right which is to work out the dimension change in the x direction but I got the y and z directions wrong. I had to submit this online and it doesn't ...
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21 views

Solving Hertz Impact ODE with Simulink

I have a question about modelling a nonlinear 2nd order ODE for an impact of a sphere on a thin plate in Simulink. Depending on the solver and solver options, my results in Matlab vary a lot. Some are ...
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29 views

Distance travelled at articulation point of turning vehicle

Problem outline: I'm trying to figure out the distance travelled at the articulation point of a turning vehicle with 4 driven wheels (each wheel houses a motor and can all rotate at different RPMs). ...
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2answers
34 views

What is the engineering way to describe a factory / manufacturing plant system in a formel and mathematical way

I am interested in mathematically describing as well as formalising a manufacturing plant so that other people in the engineering field understand how the system works. I am not from the engineering ...
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2answers
55 views

Can a simple application of two forces have two different outcomes on a rigid body?

[Summary: If two forces are such that the component of one of these forces forms a couple with the other, than which of the two cases (obtaining resultant via adding forces or obtaining moment and a ...
4
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1answer
66 views

LED Lumen Calculations

I am using an LED as a point source for a school project. I have two questions in regards to the LED(s). I know that light follows the inverse square law when measuring perceived brightness, but all ...
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1answer
93 views

Gyroscope/Powerball gearing system for bikes?

There is an interesting and potentially useful property to do with the procession of Gyroscopes, as well as devices like the "Powerball" toy. When the gyroscope is rotating (Ws) and then force is ...
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2answers
66 views

Differential equation

What are boundary conditions and initial conditions with respect to differential equation? Do they mean the same for partial differential equation? How to BC and IC vary for different types of PDE?
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2answers
78 views

How do enginners build highway interchanges ? Are highway interchanges build based on a mathematical theory such as braids and knots theory?

I am trying to find how do enginners build roads especially highway interchanges. Are they relying on any topology theories such as braids and knots theory? Is there any connection or link between ...
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0answers
36 views

Engine power and torque of a vehicle

Having the Power/Torque-RPM curves of a vehicle, how can we derive the engine power equation and the torque out of these curves with respect to time?
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1answer
67 views

Statics problem: Finding resultant force angle measured counterclockwise from positive x-axis

I have this diagram: And I have done these calculations: $$\begin{align} R_x&=-20\sin(30)+30\cos(35)+80\cos(45)=71.14\text{ lb} \\ R_y&=20\cos(30)+30\sin(35)-80\sin(45)=-22.04\text{ lb} \end{...
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2answers
205 views

Example of real-life problem solved with numerical methods? [closed]

I hope this is a suitable question to ask here. Well, I'm taking Numerical Methods this semester (also called 'Numerical Analysis' in some places). The term-assignment is to find a real-life problem ...
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1answer
95 views

Two intersecting prisms

Case 1 The development of Case 1 of this problem in which the axes of the prisms intersect at right angles, is shown in Diagram 1. Note that inter-edge lines are required for the development of both ...
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2answers
68 views

How to find the balance position of valve downstream a tank?

We have a tank which has a constant inflow of water (Qi). The level (h) of water in tank is controlled by opening/ closing (l) a valve downstream of the tank. Overflow height of the tank is 4 meter. I ...
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2answers
68 views

Working out RPM from car engine's lb ft?

Using an old copy of an automobile magazine, these are the cars with hp and lb ft I am trying to work out the RPM for: 2007 Honda Accord 2.4 sedan, 2.4-liter 187hp 4-cylinder, 164 lb ft pulling power ...
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0answers
36 views

Deriving a Time-Dependent Equation from a Surge Arrester for Transient Voltage Analysis

After looking through dozens upon dozens of IEEE papers, it seems that no one has really developed a simplified formula for a surge arrester. What I would like to be able to do is perform a transient ...
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2answers
58 views

Frequency Response of a Discrete System

Let's say that I have the following continuous system: $$G(s)= \frac{2}{1+s}$$ I could convert it to a discrete system using for example the Tustin approximation https://en.wikipedia.org/wiki/...
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1answer
30 views

impulse input and discontinuity in initial condition after

Consider a dynamical system as bellow that is subjected to an impulse input: $\sum_{n=0}^N {a_n x^{(n)}}= f_0 \delta(t-t_0)$ the initial values are non-resting (all non-zero): $x(t_0^-)=x_0\hspace{...
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1answer
76 views

Is engineering basically controlling oscillators? [closed]

When an engineer optimizes a hoe to make an excavator, what do they actually do? I guess that when they see a room for improvement of the hoe, they start solving differential equations. But as the ...
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2answers
33 views

aircraft pursuit dynamic system state update

Planar Evasive Aircrafts Maneuvers Using Reinforcement Learning $$d=\sqrt{(x_m-x_e)^2+(y_m-y_e)^2}$$ $$\dot{d} = V_e \cos (\lambda-\Psi_e) - V_m \cos(\lambda-\Psi_m)$$ $$\lambda = \arctan\frac{x_e -...
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0answers
12 views

Complete symmetric distance matrix

Is there an intuitive way to approximate/estimate missing cells in a (symmetric) distance matrix? In this case, each unknown pair has several "neighbors" for which the distance is known.
2
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3answers
91 views

Is there any defined mathematical parameter that can give me the average distance of a volume to a point?

I'm currently trying to design a bulk-handling system which minimizes the distance from the bulk material pile(s) where the material is loaded (the volume) to the unloading platform(s) (the point), ...
3
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2answers
258 views

Second Moment of Inertia (or Second Moment of Area) of Beam Section

I need to calculate the moment of Inertia Iyz but I find 0 information online about how to get it or solve it in a real problem, only that is equal to $$\bar{I}_{yz}=\int yz\text{ d}A$$ How can I ...
2
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1answer
200 views

How to work out the damping or deflection curve from deflection angles?

I have a crane boom that is rotating and when it is stopped suddenly, the boom flexes back and fourth several times. I have measured the angles between each deflection and have $3.16 ^\circ$, $2.42 ^\...
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2answers
56 views

What is the condition of real eigen values other than symmetric matrix?

I have some difficulty to solve this question: What is the condition for real eigen values other than symmetric matrix?
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2answers
82 views

Does every engineering design needs to have a complete theoretical backing or may experimental data suffice?

This may sound rather vague on its own so I will explain with examples. The solid booster rockets used by NASA space shuttle used a central bore design because it had a certain characteristic on ...
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0answers
80 views

Boundary Conditions for a circular clamped plate

I've been trying to find the boundary conditions for a fourth order DE equation for a bending circular plate. I'm assuming angular symmetry and an even pressure distribution. Displacement Equation $$...
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3answers
60 views

Mathematical connection between systems of particles and rigid bodies

This question goes right back to the first principles of mechanics, so to speak. I'm confused as to the nature of forces applied to rigid bodies. Mathematically, a force acts on a particle of a known ...
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1answer
65 views

Convert angular acceleration from (S/100Hz) to (RPM/s)

I'm writing a script that converts from a customer's preferred unit of $\frac{RPM}{s}$ and a device's input/output of $\frac{s}{100Hz}$ My Logic is as follows: Converting $\frac{RPM}{s}$ to $\frac{s}{...
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1answer
41 views

How to apply static failure criteria for bending stress in an angled cylindrical surface?

Let’s say I have an irregularly shaped bearing with a cross section that looks like the angled surface of a conical frustum, shown below. If a bending moment is applied which causes the inside ...
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1answer
125 views

Laplace Equation — Heated Plate — Heat Flux Boundary Condition

I am having a problem with transferring the heat flux boundary conditions into a temperature to be able to put it into a matrix. I understand that deltat = deltax*q''/k but I do not know how to code ...
2
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1answer
218 views

Machine design problem

I am getting confused with the maths in the max distortion strain energy part of the question. Plus there is a misprint as the formula for distortion should be a^2 +b^2-2ab=(yield stress)^2, here they ...
2
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1answer
64 views

What exactly is a proportionality?

I thought I understood what a proportionality was, but it was recently called into question. I want to make sure I fully understand how the term is generally used in the engineering world. The basic ...
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3answers
114 views

What program to implement mathematical models? [closed]

I am an engineering student and recently came upon some articles that provide numerical models that relate electromagnetic fields and temperature. I want to test out these numerical models but am ...
0
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1answer
75 views

Do triangular/area coordinates offer computational advantages for numerically integrated triangles?

Isoparametric triangular finite elements can be formulated using "triangular coordinates" $(\zeta_1, \zeta_2, \zeta_3)$, also sometimes called area/areal/barycentric coords, or using "Cartesian ...
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1answer
233 views

Is radius of gyration same for both types of moment of inertia?

We know that moment of inertia is commonly known as second moment of area. Which is $\int_{}{} y^2 dA$. However there another moment of inertia called as mass moment of inertia given by $\int_{}{} r^...
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2answers
186 views

Difference between partial derivatives and derivatives in physics [closed]

Please explain me the difference between $\lim_{x->0}\frac{\partial E}{\partial x}$ and $\lim_{x->0}dE/dx$.In physics I encountered something similar while reading about Newton's Law of Fluids....
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4answers
186 views

Is radians dimensionless quantity?

Quite often while calculating angular velocity we come across the quantity radians per second. Dimensionally how do i treat radian as?Explain vividly.