Questions tagged [mathematics]
For engineering questions involving mathematics. For pure mathematics problems, please visit our sister site Mathematics Stack Exchange.
212
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A transfer function relating jet engine thrust to pitch angle during a phugoid motion
I am doing a school project that requires me to find a transfer function that relates the thrust of a jet engine (which could change with time in one way or another) and the aircraft's pitch angle ...
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27
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How can we calculate the combined stiffness of a spline connected to a straight member?
I have a geometry that looks something like this. What will be the combined stiffness of the members?
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21
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What are the change in forces with a ribbon under tension is twisted?
Consider pallet strapping. It has width W. When the strap is flat, it has some maximum breaking strength B.
Now, let's put one twist in it over X feet. Mentally we have a VERY skinny isoceles ...
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82
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Kinematic description of a gear rack moving around a cogwheel
I am facing some issues regarding the kinematic description of a gear mechanism (or maybe more accurately gear manufacturing process). Basically I would like to obtain an animation, where the cogwheel ...
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What is the moment of inertia of a circular segment?
Hi I read this response but it isn't exactly my situation I have a circle where the axis of rotation is on the c axis like this for a segment equal to the green.
Specifically, I have a round steel ...
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Iterative Method through FEM
Due to reasons, I can not fully describe the process explicitly so I will be using substitutes to represent the variables.
Nomenclature:
x - an independent variable
y - another independent variable
Fz ...
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1
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23
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Factoring Quadratic Equations
Given a general polynomial of the form ax^2 + bx + c = 0, we can factor it to be the product of two terms eg. (x+d)*(x-e) = 0.
Why is it that we can use substitute BOTH equations as equalling zero? If ...
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Drone Geometrical Shape
Drone
Can Drones be designed with geometrical shapes viz Kite, Cylinder, Sphere etc?
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Genetic algorithm implementation for gas/power/water network operation optimizaiton
I have both practical and theoretical background in power, gas and water networks operation and I am familiar with the basics of genetic algorithm. I would like to dive into the network operation ...
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32
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How to model a driver's appropriate braking for deceleration, and throttle for acceleration for a car moving on a straight road?
A project team within my company is stuck on a conundrum and have asked me for some insights. They want to develop a driver model (mathematical or drawn) where input is the car's velocity profile, and ...
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Second moment of area (moment of inertia) for annulus segment
I am a Mechanical Engineering student and I'm working on some calculations for an assignment at a company. As a part of this assignment I need to calculate the moment of inertia (Ixx) of a segment of ...
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How to solve this thermal equilibrium
I was studying and came across a problem that I'm not sure how to solve. In fact, I think it gives me 1 degree of freedom. In the problem, I am asked to calculate the time and temperature required to ...
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Matrix Calculation
I would like to Calculate Q. The transpose of U matrix is a 2x5 matrix and U is a 5x2 matrix. Therefore, I was expecting a 5*5 Matrix, which wasn't the case. Can someone please help me to solve Q
...
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31
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Convert Azimuth and Elevation to X & Y angles
I’m trying to control a 2 axis solar tracker using a microcontroller with an internal IMU.
I can calculate sun azimuth and elevation but how do I convert them to X & Y angles that I can compare ...
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29
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How to re-write systems of two linear second order ODEs in a state space form
I have recently been working on how to convert ODES into state space form, and I came across this problem that has me confused. Should B in the state space be [1; -2] or [1 0; 0 -2]?
I think the ...
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Why is the vector cross product different here?
I was taught that the linear velocity of a body rotating around a fixed axis is the cross product between the angular velocity and the position vector.
The vector for the velocity here in this picture ...
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Calculating forces on cables
I have to calculate the pull forces of Fab and Fac.
I have used extended Pythagoras to find the length of AC and AB but I have no idea how to calculate the forces. I also tried to use cartesian ...
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91
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Rotation of point in 3D space
I want to rotate a point (3,4,5) by an angle 45 degrees(0.785398 rad) in 3D space. I have used the standard DCM matrix in the order Rx, Ry and Rz.
Where,
$\theta = 0.785398 [rad]$
$$ Rx= \begin{...
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205
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Clock pendulum period vs driving weight
I've got a weight-driven pendulum clock, I increased the driving weight by 10% and the period decreased by 1%. Why?
What's the equation?
The pendulum is
length = 32cm;
bob weight = 7g;
rod weight = 7g....
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66
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Rotation of Radar Axis in 3D plane
I'm working on a sensor fusion application.
In our vehicle, 4 radars (fixed, non-rotating radars) are placed at 4 corners of the vehicles at 45 degrees with respect to x, y and z-axes of the vehicle.
...
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How to convert PI controller in to differential equation?
I want to convert PI controller into Differential Equation form. How should I do this? Please help me.
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Force applied on a ferromagnetic shaft by a coil
I have a perfectly cylindrical ferromagnetic shaft (say, made out of iron). I want to apply an axial force on the shaft (along the centerline of the cylinder) using a coil through which an electric ...
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35
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Operations between rotating elements
Given two (or more) rotating elements, which mathematical operations can be done between them?
For example:
Different gear ratios can be used to multiply a rotating element's angular velocity by a ...
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2
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73
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How to solve for discrete state space matrices given input and output
I have a set of time-series data that consists of inputs $u_k$ where $
u \in R $ and $k = 1 ... T$, and outputs $ y_k $ where $ y \in R^2 $ and also $k = 1 ... T$, from a given system. I believe this ...
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How do I find the optimal position for a hydraulic damper to balance the force applied to a rotating assembly?
This may be a simple problem, my math and physics chops are a bit rusty.
I'm modifying a flight sim rudder pedal to add a hydraulic linear damper (specifically a motorcycle steering damper). I'm ...
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2
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624
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Is the maximum bending moment of a fixed end beam always at end?
Mathematically, we can see that with downward loads only (only upward loads at the ends), the maximum bending moment for a fixed end beam of span $L$ either occurs at $x=0$, $x=L$, or where the shear ...
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How do I find a target standard deviation for my own testing given a confidence level, a mean, and bounds for the interval?
I'm working on a project involving a couple of material dispensers, and the customer we're designing them for has asked us to keep the output of the dispensers within a set range 95% of the time. I'm ...
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651
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How do you derive the formula for converting weight percent to atom percent?
I have the following equations for weight and atom percent:
Where m is the mass of each element.
where A is the atomic weight of each element and m prime is the mass of each element.
And I'm told ...
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68
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Euler-Bernouilli for a beam with force in the middle
A beam of length $L$ is held a $x = 0, L$. A force $F$ in the middle ($x = L/2$) pushes the beam.
The Euler-Bernoulli equation can be written as such:
$EI\frac{\partial^4 y(x)}{\partial x^4} = F\delta(...
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What would the dynamics and measurement operators be in this control theory problem/code, and where can I generate them from?
I'm working on something slightly outside of my scope of work, and I can't figure out if I fully understand what these things mean. Could someone help explain what the dynamics operator and ...
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How to calculate velocity east, north up having lat/lng/alt/time?
I have a certain values from a camera and wondering how the velocity east, north and up is calculated.
Here are the values
...
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191
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What is percent of thread depth when it comes to screws?
What, geometrically, is meant by percent thread depth? And, what would constitute 100% thread depth?
I have been trying to derive the equation for thread percentage in the textbook Machine Tool ...
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158
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Maximum Deflection for simply supported beam under arbitrary triangular loading
I am trying to get the:
maximum deflection
location of maximum deflection
deflection at any point
For a beam under an arbitrary triangular load (i.e. a, b, c, and w can vary). I tried to solve this ...
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3
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108
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Use of 'parameter' in engineering?
Is there a different meaning to the word of 'parameter' in engineering? I've started in engineering from a mathematics/physics background, and commonly a 'parameter' is either used to 'parameterize' a ...
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191
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Timoshenko Fixed Fixed Total Beam Deflection
I am trying to solve a problem where there is a fixed-fixed (clamped-clamped) beam with a point load in the middle (at L/2). The L/H is less then the 10 required for normal beam bending analysis and ...
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120
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Why $\frac{m}{V}$ gives average density when density varies?
This might be a very basic question, and for years I have gone by simply accepting it as a fact. That whenever the density is uniform the formula $\frac{m}{V}$ gives that uniform value of density and ...
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Why stopping at the first derivative in conservation equations?
Oftentimes we, as engineers, have to write energy/mass/momentum balances to derive the governing equations for a quantity $\phi(x,t)$ of a physical system. One of many derivations of such balances ...
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Why are square Intergrable functions bounded? How is it related to L2 functions and Hilbert spaces?
To approximate the weak form of linear elliptic pde to solve Elasticity problem, we use L2 functions and Hilbert space. In that, I read that Square integrable functions are bounded. Why is that true ...
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99
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How to analyze strongest (honeycomb?) structure?
To be specific I have a structure consisting of a solid material (eg PLA) consisting of a top horizontal slab (eg 3 cm x 3 cm x 0.5 cm) and a bottom horizontal slab (translated vertically, of the same ...
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220
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How to calculate the degrees of freedom, constraints and the generalized coordinates in this dynamic system
The rope lengths are taken to be constant.
Solution:
$N$ particles with $k$ constraints.
. Then the Degree of Freedom (DOF) is $3N-k$.
In Figure 1, we have two particles $m_1$ and $m_2$, so $N=2$. But ...
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71
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How to calculate scaled speed
While working on a project I faced a difficult problem.
Let's say I have car at a 1/10 scale. Now if a real car drives at 10 m/s, it would take 3 seconds to travel 30m. If we look at the scaled car ...
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64
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Calculations of a sphere
I apologize if the question is very basic, I admit I'm not the best at math and physics.
I am doing an experiment with a sphere, the measurements are as follows:
The sphere has a diameter of 330 mm (...
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34
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Can the Dynosheet be read as a Fourier transform of some sorts?
I've done some quick google search on dynosheet, and what it does is that it measures the power output of the car with respect to its frequency.
My initial understanding of the dynosheet is that it ...
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How to Determine a Valid Relationship Equation Between Two Finite Datasets -- Python, Matlab or Other [closed]
I struggled to find a clear solution online so I'm resorting to asking a fresh question.
I have two finite datasets (call them 40x1 vectors) that are equal in length and generate non-linear curves, ...
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deal with algebraic loop in distributed control algorithm
Recently I found a distributed control method for multi-agent system, which implements an algebraic loop like:
$$
u_{i}=(l_{ii}+b_{i})^{-1}\left [{\sum _{j\neq i}a_{ij}u_{j} -\mu e_{2i}+b_{i} u_{0} }\...
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Should I use the rounded values given on technical drawings or work at the highest reasonable resolution?
In the image, the table of dimensions only gives a resolution of 1mm; in the actual creation of such a sign, would these approximate values be used or their true values (within reason)?
For example, R ...
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41
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Piston that produces equal amounts of swing in a lever?
I am attempting to figure out an equation I've found for designing part of Walschaerts Valve Gear. The specific implementation isn't relevant here, because it's the math I'm after, but this is the ...
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155
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Path length of a satellite signal
I am trying to work out the length of the Rsv, but I dont understand how to go about this. If the length R is known and the angle EL is known how do I go about solving for this length. I was given ...
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General Units question
so let’s say I worked out a quantity that turned out to be unit less but to work it out I used pounds (lb) and feet (ft) and the units cancelled out
But then I used this unit less number later in ...
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109
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Calculating two diagonal forces
When I tried to calculate the force exerted on the rope 'a' I get that it is equal to 5N when the block has a force of 10N. Do I instead need to divide by 30 since the sum of the two angles is 30 ...
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