<Text-field style="Heading 1" layout="Heading 1">Pure rolling</Text-field>

Roll is yawing around the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYFhfX0JgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn axis.

In pure rolling we have the following relation - the rolling rhythm 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 .

The rolling coefficient is marked by LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEoJiM4NDY2O0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy9GM1Enbm9ybWFsRic= ,

QyQ+SScmTHNjcjtHNiIsJCosSSRyaG9HRiUiIiJJIlNHRiVGKUkidkdGJSIiI0kiYkdGJUYpSSpDX18mTHNjcjtHRiVGKSNGKUYsISIi

QyQ+SSpDX18mTHNjcjtHNiIsJiomSShQX19ub3JtR0YlIiIiSSxDX18mTHNjcjssUEdGJUYpRikqJkkrJmRlbHRhO19fYUdGJUYpSTVDX18mTHNjcjssJmRlbHRhO19fYUdGJUYpRikhIiI=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1E0YENfXyZMYXBsYWNldHJmOyxQYEYnLUYsNiNRIUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== - rolling damping. Always will be narrative.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1FOYENfXyZMYXBsYWNldHJmOyxfXyZMYXBsYWNldHJmO19fLCZkZWx0YTtfX2FgRictRiw2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - force coefficient as a result of the ailerons.

In roll, the ailerons equation is:

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

We will write the forces and moment equations:

QyYvSSkmU2lnbWE7Rkc2IiomSSJtR0YlIiIiSSJhR0YlRighIiIvSSkmU2lnbWE7TUdGJSomXiNGKEYoLUklZGlmZkclKnByb3RlY3RlZEc2JS1JJHBoaUdGJTYjSSJ0R0YlRjZGNkYoRio=

From the relation presented above (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) we can see the LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRJyYjOTY2O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRiM2JS1JI21vR0YkNi1RIy4uRidGNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHUSYwLjBlbUYnL0YzUSV0cnVlRicvRjZRJ2l0YWxpY0YnL0ZLRlNGNQ== equals to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkmbW92ZXJHRiQ2JS1JI21pR0YkNiVRIlBGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictRiM2JS1JI21vR0YkNi1RIi5GJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkIvJSlzdHJldGNoeUdGQi8lKnN5bW1ldHJpY0dGQi8lKGxhcmdlb3BHRkIvJS5tb3ZhYmxlbGltaXRzR0ZCLyUnYWNjZW50R0ZCLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdGUUYyRjUvRk5GNEY+ , and therefore, the moment expression is

QyQ+SSkmU2lnbWE7TUc2IiomSSVJX194R0YlIiIiLUklZGlmZkclKnByb3RlY3RlZEc2JC1JIlBHRiU2I0kidEdGJUYwRighIiI=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

and we know that 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

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

QyQ+SSRlcTFHNiIvSSkmU2lnbWE7TUdGJUknJkxzY3I7R0YlISIi

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PkkkZXEyRzYiLUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLUkoaXNvbGF0ZUdGJDYkSSRlcTFHRiRJKFBfX25vcm1HRiQ=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTJHRigvSShQX19ub3JtR0YoLCYqMEksQ19fJkxzY3I7LFBHRighIiJJJUlfX3hHRigiIiItSSVkaWZmR0YmNiQtSSJQR0YoNiNJInRHRihGPEY1SSRyaG9HRihGM0kiU0dGKEYzSSJ2R0YoISIjSSJiR0YoRjMiIiMqKEYyRjNJKyZkZWx0YTtfX2FHRihGNUk1Q19fJkxzY3I7LCZkZWx0YTtfX2FHRihGNUYzNyNGLg==

In order to solve the following ODE we need to define LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EqYFBfX25vcm1gRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn and the initial conditions.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

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And the rolling rhythm LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EqYFBfX25vcm1gRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn is LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

QyQvSShQX19ub3JtRzYiKihJIlBHRiUiIiJJImJHRiVGKC1JIi9HNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiU2IywkSSJ2R0YlIiIjRighIiI=

The initial conditions:

QyQ+SSRJQ1NHNiIvLUkiUEdGJTYjIiIhRiohIiI=

Arranging the variables:

PkkkZXEzRzYiLUknZXhwYW5kRyUqcHJvdGVjdGVkRzYjLCQqKC1JKGFsZ3N1YnNHRiQ2JC9JKFBfX25vcm1HRiQqKC1JIlBHRiQ2I0kidEdGJCIiIkkiYkdGJEY1LUkiL0c2JEYnSShfc3lzbGliR0YkNiMsJEkidkdGJCIiI0Y1SSRlcTJHRiRGNUY9RjVGNiEiIkY+

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTNHRigvLUkiUEdGKDYjSSJ0R0YoLCYqMEkidkdGKCEiIkkiYkdGKCEiI0ksQ19fJkxzY3I7LFBHRihGNkklSV9feEdGKCIiIi1JJWRpZmZHRiY2JEYvRjJGO0kkcmhvR0YoRjZJIlNHRihGNiIiJSosRjVGO0Y3RjZGOUY2SSsmZGVsdGE7X19hR0YoRjtJNUNfXyZMc2NyOywmZGVsdGE7X19hR0YoRjtGODcjRi4=

We pack all the constants in one variable:

NiQvSSZwX19zc0c2IiwkKixJInZHRiUiIiJJQENfXyZMc2NyOyxfXyZMc2NyO19fLCZkZWx0YTtfX2FHRiVGKUkrJmRlbHRhO19fYUdGJUYpSSJiR0YlISIiSSxDX18mTHNjcjssUEdGJUYtIiIjL0kpJnRhdTtfX1JHRiUsJCouSSVJX194R0YlRilGKEYtRiwhIiNGLkYtSSRyaG9HRiVGLUkiU0dGJUYtIiIl

So the differential equation is:

PkkkZXE0RzYiLy1JIlBHRiQ2I0kidEdGJCwmKiZJKSZ0YXU7X19SR0YkIiIiLUklZGlmZkclKnByb3RlY3RlZEc2JEYmRilGLSEiIkkmcF9fc3NHRiRGLQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTRHRigvLUkiUEdGKDYjSSJ0R0YoLCYqJkkpJnRhdTtfX1JHRigiIiItSSVkaWZmR0YmNiRGL0YyRjYhIiJJJnBfX3NzR0YoRjY3I0Yu

So the solution of the differential equation is:JSFHJSFH

PkklUm9sbEc2Ii1JKXNpbXBsaWZ5R0YkNiMtSSdkc29sdmVHRiQ2JDwkSSRJQ1NHRiRJJGVxNEdGJC1JIlBHRiQ2I0kidEdGJA==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVSb2xsR0YoLy1JIlBHRig2I0kidEdGKCwkKiZJJnBfX3NzR0YoIiIiLCYtSSRleHBHRiU2IywkKiZJKSZ0YXU7X19SR0YoISIiRjJGNkY+RjZGPkY2RjZGPjcjRi4=

LUklZXZhbEclKnByb3RlY3RlZEc2JEklUm9sbEc2IjwkL0kmcF9fc3NHRicsJCosSSJ2R0YnIiIiSTVDX18mTHNjcjssJmRlbHRhO19fYUdGJ0YuSSsmZGVsdGE7X19hR0YnRi5JImJHRichIiJJLENfXyZMc2NyOy5QR0YnRjIiIiMvSSkmdGF1O19fUkdGJywkKi5JJUlfX3hHRidGLkYtRjJGMSEiI0ksQ19fJkxzY3I7LFBHRidGMkkkcmhvR0YnRjJJIlNHRidGMiIiJQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Ly1JIlBHNiI2I0kidEdGJSwkKi5JInZHRiUiIiJJNUNfXyZMc2NyOywmZGVsdGE7X19hR0YlRitJKyZkZWx0YTtfX2FHRiVGK0kiYkdGJSEiIkksQ19fJkxzY3I7LlBHRiVGLywmLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlNiMsJCowSSVJX194R0YlRi9GKkYrRi4iIiNJLENfXyZMc2NyOyxQR0YlRitJJHJob0dGJUYrSSJTR0YlRitGJ0YrI0YvIiIlRitGL0YrRishIiM=

JSFH

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHRfX2ZgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - the time of the total rolling.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHRfX3NgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn - the time we need to pull the stick to the other side (when we switch the ailerons from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ExYCZkZWx0YTtfX2EsbWF4YEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1ExYCZkZWx0YTtfX2EsbWluYEYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJw== ).

Does during a maneuver 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?

The answer is NO! we need to take into consideration that during the maneuver one side of the aircraft has more wind influence than the other, therefore, 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.

The example below shows the aileron angle change during the rolling. In this example we set the rolling time to be 20 sec.

LUklcGxvdEc2IjYoLUkqcGllY2V3aXNlRyUqcHJvdGVjdGVkRzYmMkkieEdGJCIjNyIiJjMtSSI+R0YoNiQiIz9GKy1JIz49R0YoNiRGK0YsISImL0YrOyIiISIjRC9JInlHRiQ7ISInIiInL0kmY29sb3JHRiRJJHJlZEdGJC9JJ2xhYmVsc0dGJDckLiomSSV0aW1lR0YoIiIiNyNJJHNlY0c2JEYoSShfc3lzbGliR0YkRkkuKiZJKyZkZWx0YTtfX2FHRiRGSTcjSSRkZWdHRiRGSS9JKmxhYmVsZm9udEdGJDclSSZBcmlhbEdGJEklQm9sZEdGJCIjOw==

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

We can divide the figure above to two parts I (max angle) and II (minimal angle). We will show what happens in every part:

Part I - LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX2FgRictSSNtb0dGJDYvUSI9RicvJSVib2xkR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y4LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2I1ExYCZkZWx0YTtfX2EsbWF4YEYnLyUwZm9udF9zdHlsZV9uYW1lR1EqSGVhZGluZ34yRicvRjdRJ25vcm1hbEYn

JSFH

Part II - LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2I1EtYCZkZWx0YTtfX2FgRictSSNtb0dGJDYvUSI9RicvJSVib2xkR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y4LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2I1ExYCZkZWx0YTtfX2EsbWluYEYnRjMvJTBmb250X3N0eWxlX25hbWVHUSpIZWFkaW5nfjJGJ0Y2Rjk=

QyQ+SShwX19zcyxJRzYiLCQqLEkidkdGJSIiIkk1Q19fJkxzY3I7LCZkZWx0YTtfX2FHRiVGKUkvJmRlbHRhO19fYSxtYXhHRiVGKUkiYkdGJSEiIkksQ19fJkxzY3I7LFBHRiVGLSEiI0Yt

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

We set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EqYHBfX3NzLElgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EsYHBfX3NzLG1heGBGJ0Yz and get:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

PkklUF9fSUc2Ii1JJXN1YnNHJSpwcm90ZWN0ZWRHNiQvSSZwX19zc0dGJEkqcF9fc3MsbWF4R0YkLUkkcmhzR0YnNiNJJVJvbGxHRiQ=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSVQX19JR0YoLCQqJkkqcF9fc3MsbWF4R0YoIiIiLCYtSSRleHBHRiU2IywkKiZJKSZ0YXU7X19SR0YoISIiSSJ0R0YoRjFGOUYxRjlGMUYxRjk3I0Yu

JSFH

QyQ+SSlwX19zcyxJSUc2IiwkKigsJiomSSJ2R0YlIiIiSTVDX18mTHNjcjssJmRlbHRhO19fYUdGJUYrIiIjLUkkYWJzRyUqcHJvdGVjdGVkRzYjSS8mZGVsdGE7X19hLG1heEdGJSEiIkYrSSJiR0YlRjNJLENfXyZMc2NyOyxQR0YlRjNGM0Yz

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

We set LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1ErYHBfX3NzLElJYEYnLUkjbW9HRiQ2LVEiPUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOC8lKXN0cmV0Y2h5R0Y4LyUqc3ltbWV0cmljR0Y4LyUobGFyZ2VvcEdGOC8lLm1vdmFibGVsaW1pdHNHRjgvJSdhY2NlbnRHRjgvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZHLUYwNi1RKiZ1bWludXMwO0YnRjNGNkY5RjtGPUY/RkFGQy9GRlEsMC4yMjIyMjIyZW1GJy9GSUZOLUYsNiNRLGBwX19zcyxtYXhgRidGMw== and get:

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

PkkmUF9fSUlHNiItSSVzdWJzRyUqcHJvdGVjdGVkRzYkL0kmcF9fc3NHRiQsJEkqcF9fc3MsbWF4R0YkISIiLUkkcmhzR0YnNiMtSSlzaW1wbGlmeUc2JEYnSShfc3lzbGliR0YkNiMtSSdkc29sdmVHRjM2JEkkZXE0R0YkLUkiUEdGJDYjSSJ0R0Yk

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSZQX19JSUdGKCwmSSpwX19zcyxtYXhHRighIiIqJi1JJGV4cEdGJTYjLCQqJkkpJnRhdTtfX1JHRihGMEkidEdGKCIiIkYwRjlJJF9DMUdGKEY5Rjk3I0Yu

JSFH

Now, in order to find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHRfX3NgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn we know that this is the time when LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2I1EnYFBfX0lgRictSSNtb0dGJDYtUSI9RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y4LyUpc3RyZXRjaHlHRjgvJSpzeW1tZXRyaWNHRjgvJShsYXJnZW9wR0Y4LyUubW92YWJsZWxpbWl0c0dGOC8lJ2FjY2VudEdGOC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkctRiw2I1EoYFBfX0lJYEYnRjM= so:

PkkkZXE0RzYiLUklc3Vic0clKnByb3RlY3RlZEc2JC9JInRHRiRJJXRfX3NHRiQvSSVQX19JR0YkSSZQX19JSUdGJA==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRlcTRHRigvLCQqJkkqcF9fc3MsbWF4R0YoIiIiLCYtSSRleHBHRiU2IywkKiZJKSZ0YXU7X19SR0YoISIiSSV0X19zR0YoRjJGOkYyRjpGMkYyRjosJkYxRjoqJkY0RjJJJF9DMUdGKEYyRjI3I0Yu

We can isolate the constant and get:JSFH

LUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy1JKGlzb2xhdGVHRiQ2JEkkZXE0R0YnSSRfQzFHRic=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

L0kkX0MxRzYiLCQqKEkqcF9fc3MsbWF4R0YkIiIiLCYtSSRleHBHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiQ2IywkKiZJKSZ0YXU7X19SR0YkISIiSSV0X19zR0YkRihGM0YoISIjRihGKC1GKzYjRjFGKEYz

We know that LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EoYFBfX0lJYEYnLUkobWZlbmNlZEdGJDYkLUYjNiYtRiw2JVEidEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RIj1GJy9GO1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRkUvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGVC1GLDYjUSdgdF9fZmBGJ0ZBRkFGPS1JI21uR0YkNiRRIjBGJ0ZBRkE= , therefore:

LUkpc2ltcGxpZnlHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2Iy1JJXN1YnNHRiU2JS9JJF9DMUdGJywkKihJKnBfX3NzLG1heEdGJyIiIiwmLUkkZXhwR0YkNiMsJComSSkmdGF1O19fUkdGJyEiIkkldF9fc0dGJ0YxRjlGMSEiI0YxRjEtRjQ2I0Y3RjFGOS9JInRHRidJJXRfX2ZHRicvSSZQX19JSUdGJyIiIQ==

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

LywkKiZJKnBfX3NzLG1heEc2IiIiIiwoLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsJComSSkmdGF1O19fUkdGJiEiIkkldF9fZkdGJkYnRjJGJy1GKjYjLCQqJiwmRjNGJ0kldF9fc0dGJkYyRidGMUYyRjIhIiNGJ0YnRidGMiIiIQ==

Isolating LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHRfX3NgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn from the equation above:

PkkldF9fc0c2Ii1JKXNpbXBsaWZ5RzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMtSSZzb2x2ZUdGJzYkLywkKiZJKnBfX3NzLG1heEdGJCIiIiwoLUkkZXhwR0YnNiMsJComSSkmdGF1O19fUkdGJCEiIkkldF9fZkdGJEYyRjpGMi1GNTYjLCQqJiwmRjtGMkYjRjpGMkY5RjpGOiEiI0YyRjJGMkY6IiIhRiM=

LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2JVE1b3V0cHV0fnJlZGlyZWN0ZWQuLi5GJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRic=

print(); # input placeholder

Warning, solving for expressions other than names or functions is not recommended.

LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSV0X19zR0YoLCgqJkkpJnRhdTtfX1JHRigiIiItSSNsbkdGJTYjIiIjRjEhIiIqJkYwRjEtRjM2IywmLUkkZXhwR0YlNiMsJComRjBGNkkldF9fZkdGKEYxRjZGMUYxRjFGMUYxRkBGMTcjRi4=

So, assuming we have the whole roll time LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHRfX2ZgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn we can find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EnYHRfX3NgRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn .

From the relation shown above between the roll angle and the roll rhythm we can find LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2JVEnJiM5NjY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJ0Yy :

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

JSFH