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Questions tagged [mathematics]

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2answers
52 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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48 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
25 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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0answers
45 views

Area moment of inertia calculation

I have a planar lamina which is swept through helical curve. I want to calculate area moment of inertia at every section plane. But the orientation of the planar lamina is changing at every section ...
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0answers
26 views

Beam Defelction Using Macaulay Theorem

I have a simply supported beam and am trying to work out the deflection using Macaulay's Theory, is it possible to verify my results, I feel they are far out, and can not see where the error lies. ...
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0answers
41 views

What kinds of math do I need to know before I study mechanical engineering?

I know this isn't a question about a direct mechanical engineering project question, but I'm hoping this is considered a question that can be answered and isn't closed. I'm new to mechanical ...
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0answers
21 views

Constructing a proper Finite Difference Scheme for 3-dim function using data

$$f(x,y)$$ $f$ is unknown and I want to estimates its derivatives $$\frac{\partial f}{\partial y}, \frac{\partial f}{\partial x} \text{ and } \frac{\partial f}{\partial x^2}$$ from a data set. I have ...
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1answer
26 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
38 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
42 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
48 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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0answers
20 views

Doubt regarding relation between maximum of $||x||$ and $x^TAx$ with regards to attitude dynamics

I was dealing with 3-DOF attitude dynamics of rigid body and wanted to comment upon the following defined function $F$ at its maxima. Consider $F \in \mathbb{R} : F(e_{\Omega}(t)) = \frac{1}{2}e_{\...
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2answers
64 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
18 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
52 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
26 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
72 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
31 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
10 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.
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3answers
84 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), ...
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2answers
170 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 ...
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1answer
61 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
54 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
69 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
35 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
54 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
55 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
28 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
92 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
154 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
45 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
86 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 ...
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1answer
53 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
140 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
100 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
156 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.
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0answers
103 views

How to integrate ∫vᵢ(uᵢ² + vᵢ²)dA in calculating monosymmetry index of an angle?

I saw this question asking about calculating monosymmetry index of an unequal angle. What I need is a formula to calculate $\int v_i{(u_i}^2 + {v_i}^2)\text{d}A$, given the depth $d$, breadth $b$ and ...
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0answers
24 views

Objectivity vs Symmetry for a Function

I'm learning about objectivity/frame invariance in continuum mechanics, but I'm having a little trouble grasping the concept. In the case of a scalar valued function $\phi: \mathbb{R}^3 \rightarrow \...
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27 views

Strain relations for axisymetric problems

I've seen on a book that the following relation holds for axisymmetric problems: $$\varepsilon_r=\varepsilon_{\theta}$$ where $\varepsilon_r$ and $\varepsilon_{\theta}$ are, respectively, the radial ...
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1answer
60 views

Does engineering require extensive math? [closed]

I hope this question is okay for here. I've been interested in engineering for quite some time, but havent really ever had the motivation to do anything about it. I took a small principles of ...
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2answers
27 views

How to duplicate measurements from one piece of material to another?

I am not sure if this is the right place to ask this but. I have an offroad skateboard from MBS. I bought their brake system which comes with a circular piece of aluminum. Pictures attached. You can ...
2
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1answer
65 views

Wing as cantilever beam (beam-rod) model for aeroelasticity fluttering analysis

I recently bumbped into a rather basic but interesting question on aeroelasticity. I've learned to derive the fluttering critical speed from Pines's theory but it involves some spring stiffness like ...
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1answer
138 views

Darcy to SI permeation units

How can permeation units in Darcy be converted to the SI form. For example, how would 9.0 x 10-6 darcy be converted to SI units of permeation? How would it also be converted to the permeation units: (...
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3answers
77 views

Graphene distribution over a sphere

How much graphene is required to coat a 5 inch (diameter) sphere if the graphene layer must be 35 nanometers thick?
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1answer
206 views

Two-way pulley system considering inertia of pulleys

This is the following question. [![This is how i tried, but I know it is wrong.][2]][2] This is our attempt but We can't seem to solve it with inertia.
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1answer
95 views

Two angular velocities on two segments connected by a hinge joint differ only by the joint angle velocity

I was reading this article called "Joint Axis and Position Estimation from Inertial Measurement Data by Exploiting Kinematic Constraints", but I'm not understanding one part, which doesn't let me ...
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2answers
169 views

3D Transformation Between Two Cartesian Coordinate Systems Using Euler Angles

I am trying to transform any arbitrary vector $\bf{v_{1}}$ in a Cartesian frame $\mathscr{F_{1}}$ into a different Cartesian frame $\mathscr{F_{2}}$. Both $\mathscr{F_{1}}$ and $\mathscr{F_{2}}$ have ...
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2answers
59 views

Center line of cut-off periodic signal

What I am after is the center line of this wave, which is 0. How can I calculate that value though? For example, run the code below for a simple example in Matlab. This will plot a simple sine wave ...
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2answers
103 views

Moments of inertia, rods mechanism

I need some assistance understanding moments of inertia. I am doing some review for an upcoming exam, however I am slightly stumped by this question. I have already tried googling "moments of inertia" ...
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0answers
388 views

Industrial applications of vector calculus [closed]

I'll be teaching vector calculus to mechatronics engineers, and I'd like to provide them with industrially relevant examples, especially of the use of vector fields. Can anyone suggest either an ...