# bc0n/simbodyExamples

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C++ Matlab
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 Failed to load latest commit information. README.md findPeaks.m verifyDynamics.cpp verifyDynamics.csv verifyDynamics.m verifyDynamics.png

# simbodyExamples

I'm testing Simbody for mechanical system modeling, here are some quick notes. Also on my website

## VisualStudio 2016 setup

I followed the x64 VisualStudio instructions, placing the final installation in C:\Simbody. After creating a new C/C++ Win32 Console Application and a blank source file (to access the C/C++ options), I entered these project properties:

Configuration Properties | VC++ Directories | Executable Directories = C:\Simbody\bin

Configuration Properties | C/C++ | All Options | Additional Include Directories = C:\Simbody\include

Configuration Properties | Linker | All Options | Additional Library Directories = C:\Simbody\lib

Configuration Properties | Linker | All Options | Additional Dependencies = libblas.lib;liblapack.lib;pthreadVC2_x64.lib;SimTKcommon.lib;SimTKmath.lib;SimTKsimbody.lib (all in the lib directory)

I'm no expert on VS; the above work for me.

## A basic check of the dynamics

Let's model the elementary mass/spring/damper system and calculate the natural frequency and damping from the response. See the many comments in verifyDynamics.cpp. Included there is a basic PositionReporter that writes positions into a given text file.

The values given in the cpp allow calculation of the system's response, with some relevant parameters being: $\omega_n = \sqrt{\frac{K_{spring}}{M}} = 2.2361$ [rad/s] $\zeta = \frac{C_{damp}}{2 \sqrt{K_{spring}M}} = 0.0112$ (underdamped) $\omega_d = \omega_n \sqrt{1-\zeta^2} = 2.2359$ [rad/s]

Now, let's measure these same parameters from the simulated response. Running verifyDyanmics.cpp produces a csv file with the x position written out every 0.1sec. Plotting this in Matlab gives verifyDynamics.png.

The response is the black line, with blue x's indicating the identified peaks and valleys. The dashpot causes the initial 10m/s velocity to decay exponentially, with the response envelope given by $A e^{-\zeta \omega_n t}$. If we measure the time between peaks or valleys, we find the damped time constant $t_d$, which is related to the damped natural frequency by:

$\omega_d = \frac{2\pi}{t_d} = 2.3639$ versus $2.2359$ calculated above.

The above response also draws the envelope function, with the cyan giving the calculated envelope and the red dashed Matlab's 1D exponential estimate.

So, this was a very simple check on Simbody's physics and a good excuse to figure out how to easily move data out of Simbody.