Questions tagged [dynamics]

Questions about the dynamics of a system. Currently there is a very large scope ranging from from dynamics in mechanics, vehicle and flight dynamics, to system dynamics and fluid dynamics.

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Gravitation Potential Energy on Sector Gears

Find an equivalent spring stiffness for a system using Energy Methods. The problem is, I do not understand when gravitational potential energy should be taken into account. Let's see the examples ...
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Question about engine reaction torque from gas forces

in the figure below the reaction torque equation is given by Fg41.x trying to rock the ground plane about the O2 pivot due to gas forces . My question is if the piston with the cylinder whole assembly ...
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Difference between body-fixed angular velocity and the rate of change of Euler angles?

I'm visualising the motion of a rigidbody in 3D space with MATLAB and Simulink using this library which implements 6DOF equations of motion based on applied forces and moments. Here is my model so far ...
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Sign Convention for Energy Methods in Vibration Analysis

Find the equivalent spring stiffness of the system below. I was able to solve it using Newton's second law and got the result below. $$ k_{eq} = \frac{mgl}{2} - \frac{k_1 l^2}{16} - k_2 l^2$$ However,...
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How to get correct yaw and pitch after rotation

I am trying to come up with a "stabilization" algorithm for an antenna dish. The dish can move in the azimuth (yaw) and elevation (pitch) directions. But the boat it is mounted to, moves in ...
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What is the effect of caster angle in automobiles? What will happen if we use neutral caster?

What is the effect of caster angle in automobiles and what will happen if we use neutral caster? We study that positive caster makes vehicle more stable at high speeds. It increases lean while ...
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Entrainment Speed in Ball Bearing

Assuming no slip between the inner race and the outer race of a ball bearing, what is the entrainment speed between the balls and the inner race? The inner race is rotating at $\omega_i$ and the outer ...
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Clarification of a piston and crank dynamics question

Yesterday, I had an Engineering Mechanics exam which involved a Piston and a Crankshaft engineering dynamics problem, which I was a bit stumped about. I sought clarification from the teaching staff ...
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Spring and damper in series, equation of motion

For the motion in fig 4.1 (a), please check the description of this system in the images above, everything should be there. I get it, assuming the positive direction is downward, the spring tension is ...
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How to replace these two forces with one force?

Here, $P>Q$. $O$ is the center of mass of the rigid and uniform bar/stick. As $P>Q$, the resultant is situated to the right of $\vec{P}$ and is parallel to $\vec{P}$. The magnitude of the ...
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Estimating yaw torque and power of HAWTs

I am trying to estimate the amount of torque and power required to rotate a 3 bladed Horizontal Axis Wind Turbine (HAWT) about a vertical axis("yaw" motion). I would like to estimate the ...
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The physical principle behind short recoil operation in guns

Introduction I'm interested in the underlying physics of the recoil-operated loading mechanism in a general rifle system (e.g. M107A1 rifle). A technical of the rifle can be found on wikipedia https://...
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Total Kinetic Energy of a System with a Body Inside Another for Lagrange's Equation

Suppose a bus with mass $m_1$ moving horizontally with velocity $\dot{x}_1$, and a person with mass $m_2$ running with velocity $\dot{x}_2$ inside the vehicle. What is the total kinetic energy of the ...
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How to model the state space matrix of a pendulum?

Here's an image of the problem: I'm trying to put the following problem in matrix form (state space) but I don't know how would I put -(g/L)sin(x1) in the A matrix since the x1 value is inside the ...
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How to draw a free body diagram of a cylinder under torsion?

What is the correct way to draw a free body diagram (FBD) for the following cylinder? Assume the cylinder and disc have been twisted to an angular deflection of $\theta$. Further assume that we are ...
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Frictional wheels without slipping (gear system)

In the figure below it is stated that the friction force should always be greater than the tangential force in order to prevent slipping between two frictional wheels. My question is that if we apply ...
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Modelling a Simple Translational System

I posted this on stack exchange physics, sadly no one has answered so I thought I'd try my luck here. I am trying to model the following translational mechanical system in I/O form, however I am ...
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Relationship between the infinity norm of estimation error and the trace of estimation error covariance matrix in Kalman filter

I am working on designing an interconnected distributed control system. In this system, I need to use Kalman filter because the measurements are noisy. I have two questions: 1 - What is the ...
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Rigid-flexible multibody dynamic coupling terms

Suppose a multibody consisting a rigid and a flexible parts. When the rotation dynamic of the rigid and flexible part are derived, we see angular acceleration of rigid part, $\ddot{\theta}$ in ...
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Is this kind of steering possible?

I would like to build a small robot and was wondering if a particular configuration of steering would even be possible and stable. What I would like is to have the two rigid axles mounted on a ...
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1 answer
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Peristaltic pump - theory vs reality, where is a problem?

I'm building a test system (experiment) for peristaltic pump to check if pump is able to pump according to specification. The pump data: 6,3ul liquid moved per stroke. 5 strokes per revolution. The ...
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2 answers
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How does one deal with indeterminacy in modeling the motion of vehicles with multiple wheels? (Dynamics Question)

Consider a vehicle with four wheels and suspension (coil and dampers) rolling over an arbitrary surface. What would be the magnitude (not direction) of the normal force on each wheel? Is there a ...
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Easy software for : Multibody dynamics of rigid bodies?

I am currently searching for an easy-to-use tool to understand/simulate multibody dynamics of rigid bodys. I have no engineering or mechanics background (I am from IT) and I feel that I cannot imagine ...
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Time Constant For Step Response First Order System

I ran several experiments where I attached my phone to a motor and collected the angular velocity at different step inputs( different voltage values). My question is, is it possible for the motors to ...
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2 answers
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Torque Required From Motor For a Project

The device I am building is responsible for supporting 200 lbs and is required to accelerate 10 feet per second. The device will have two 8 inch diameter wheels. I have worked out what I believe to be ...
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1 answer
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Modeling the Internal Forces Exerted on a Catapult Arm while Throwing

I am currently creating a MATLAB script to determine the internal forces present in a uniform beam as it is accelerated by a torsional spring. I was able to derive the equation for the axial force ...
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2 answers
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Control System Response

How does one find the zeta value or the frequency of an over damped response curve. I am used to determining things by using the log-decrement equation. Does that apply here even though there is no ...
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3 answers
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Is there a simple trigonometric relationship between these two angles?

The setup shows 3 rigid links (with fixed lengths) constrained by 4 joints. The blue joints are fixed in place and only allow rotation, while the black joints can move and also allow rotation. ...
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How can you make a solid box jump up with no external forces?

Let's say I have a box lying on a flat surface. Inside the box, I make a heavy mass hang from a spring attached to the top of the box. If we pull the mass all the way down and let it go, I believe it ...
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Is there an equation that can automatically tune a PID controller?

Is there an equation that can automatically tune PID controllers? or do I have to do manually/make an AI to do it for me?
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Rover Steering Torque

I would like to calculate the required motor torque to turn a rover wheel whilst the rover is stationary. I have modelled the friction force as a distributed force acting equally along the width of ...
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How long does it take and how far does it travel a sphere in free fall before reaching a percentage of the terminal velocity?

Assume a sphere (hail) that is free dropping in air. At some the sphere will reach close to the terminal velocity. The question is: how long $t_p$ in seconds does it take before a percentage $p$ of ...
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1 vote
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Does the terminal velocity of a sphere in free drop increase with increasing diameter?

I was trying today to calculate the terminal velocity of a hailstones with increasing diameter and mass. I was trying to figure out if larger hailstones will have a higher impact velocity or lower. I ...
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4 answers
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A question on resonance

This is to settle a debate. I was working on a scaffold next to a building, as the wind blew, the scaffolding would sway. As I stood there I was trying to maintain my stability, but my movements ...
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1 answer
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Question about a Force in FBD of a garage door

I am not sure how to draw a certain force in a FBD (Free Body Diagram) of a garage door. The Garage door is indicated by B-C (2m height) in the picture below. If this door is closing, how should the ...
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3 votes
1 answer
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How is rack and pinion steering configured for different wheel/axle spacing?

The rack and pinion is supposed to turn each of the front wheels differently, such that lines orthogonal to the wheels will intersect in line with the rear axle: Which components of the rack and ...
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1 vote
1 answer
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Why is the sum of binormal forces equal to zero?

I've read in Hibbeler Dynamics, page 131, that when considering a coordinate system with normal and tangential axes, the sum of binormal forces equals zero. I don't understand why this is true, maybe ...
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3 votes
1 answer
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Modeling rigid body dynamics: Trouble with equations, encountering nonsense answers

Hi, I am working on modeling a simple rigid body dynamic system through a certain range of motion. Here is the picture of the system. I am trying to solve the system for the variables $x_1'', y_1'', ...
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2 votes
0 answers
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Plane Wave Expansion method

I have very recently ventured into the domain of periodic structures. In the literature, I came across the Plane Wave Expansion method to compute the dispersion curves. I managed to code it in 1D . ...
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3 votes
1 answer
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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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2 votes
1 answer
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Free body diagram of a differential-drive mobile robot

I'm trying to study the free body diagram of this differential-drive mobile robot in case of straight trajectory (same torque applied on both of rear wheels) and pure rolling motion I started ...
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1 vote
2 answers
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is a positive acceleration indication that velocity must be positive?

the question is clear and straight forward but when i get the velocity it should be ±√2 what i don't understand is the guide answer refusing the -ve value because acc is always +ve thank you in ...
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2 votes
1 answer
61 views

Determine the minimum horizontal force to disturb the equilibrium

Three blocks of 1N 2N and 3N are placed one over the other respectively. If the friction between the topmost 1N and the middle 2N block is twice the friction between the lowest 3N and floor then ...
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1 vote
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Increasing convergence rate using Optimal Control and Pontryagin Maximum Principle

My question is in addition to Tuning the optimal control synthesized according to the Pontryagin maximum/minimum principle and choosing the cost function, but requires help from the mathematical side ...
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How to get the normal acceleration

For the problem below, I tried solving it, but I don't know where I should get the value of normal acceleration, guess I was lost. And here's what I solved so far
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1 answer
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Why does my trimmer feels heavier when it is operating and its fully charged?

I have a Philips trimmer which when fully charged feels much heavier than when it is not charged. Also , the blades move much faster when it is fully charged I.e it’s weight , speed of blades kind of ...
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Input signal rescaling block [closed]

The input signal is limited and lies in range $[-U;+U]$. $U$ - unknown. The output signal must be rescaled to be in the range $[-1;+1]$, i.e. is $+1$ if the input is at steady-state $+U$, and $-1$ if ...
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Find a constraint relation for this Q of 3 pulleys and 2 blocks attached with string

Using any method find the constraint relation between mass 1 and mass 2. Assumptions: No friction , massless string and pulley. Q: Find constraint relation between 1kg and 2kg block. what I tried so ...
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2 votes
1 answer
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How do engineers reduce vibration of system with multiple known natural frequencies? How do they design the isolation system for specific frequencies?

I have a system that is pretty much a chamber that needs to sit on the ground. I measured the transmissibility of the chamber vs the ground (output/chamber acceleration over input/ground acceleration) ...
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1 vote
1 answer
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Trajectory of the center of mass of a vehicle

The problem is to find the trajectory of the center of mass of a car when it is rotating and translating (after an off center collision, for instance) What i know as input is the trajectory of the ...
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