# Questions tagged [mathematics]

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### Transfer of torque from the reaction wheel to the satellite body in SolidWorks

I am modeling the impact of the moment of a reaction wheel mounted on the z-axis on the body of a satellite in Solidworks. The problem is that the moment from the reaction wheel is not transmitted to ...
• 232
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### Simulation of the gyroscopic effect in SolidWorks Motion

Has anyone tried to simulate the gyroscopic effect in SolidWorks Motion? Is the effect reproducible? Share your knowledge and experience, please. EDIT: I was trying to get something like this. https:/...
• 232
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### How to derive the expression for number of teeth in virtual spur gears

Several literary sources express the number of teeth of a virtual gear by the following equation $$z_v = \frac{z}{\cos^3 \beta} \tag{1}$$ where the derivation is based on the radius of osculating ...
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1 vote
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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....
81 views

### 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. ...
171 views

### 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.
37 views

### 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 ...
108 views

### 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 ...
65 views

### 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 ...
1 vote
1k views

### 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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1 vote
94 views

### 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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1k views

### 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 ...
93 views

### 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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