Mathematics Solution Help Please Needed
Budget: $30 – $250 USD
Hello,
Not being in a math classroom for some 50 years now, I am struggling to find the most proper solution for the following. It requires some math/geometry and/or perhaps physics knowledge that I have likely forgotten (or never learned to begin with).
Attached Figure 1 shows one example that needs to be adequately solved for. It is a preliminary analysis of upward movement of an object away from the ground, represented in vector form and as selected from video frames of the movement. At frame 170 (the green 170 circle and starting point), both vectors are one and the same. The movement then progresses through frame 185 (the green 185 circle and end of the desired analysis period).
Two notable movement types have taken place. One is a rotational aspect that creates a rotation point location (intersection) among the two vectors (the red 185 circle). The other is a generalized (translational?) aspect. In this case, the vector as a whole moves somewhat upward and to the right over the course of the period. Two items I do recall/retain are that if only the rotational aspect were present, then vector segment lengths from their top ends to the red 185 circle would be equal, and the top end of vector 185 would reside slightly below a line drawn perpendicular to the top end of vector 170.
It is the rotational component(s), and more specifically the rotation point location (intersection) among the two vectors, that essentially needs to be isolated as precisely as possible from the total vector movement(s). The rotation point location is critically used toward determining an effective weight of the object sensed over the course of the movement.
And in this case, because of the translational vector movement(s) also taking place, the calculated rotation point location (again the red 185 circle) is quite erroneous compared with where it actually is. Through vast experience, the actual rotation point location in this specific example is substantially lower than displayed. This is largely confirmed in Figure 2, which analyzes just the first few frames (170-172) of the same specimen. Luckily in this instance, it appears to indicate some very early rotation (red circles), before any notable translational movement begins that routinely and greatly influence calculated rotation point locations.
Now it is possible that I have come across a relatively simple yet effective solution at this point. Elements of that work can be seen in attached Figure 3. I would be glad to address any questions or comments regarding what I did there. Unfortunately, however, I am not especially confident in the results I have been getting, particularly when applying it to other test specimens. So I am not yet able to confidently move any further along with the project.
This is partly because more recently I determined an alternative solution or two that measurement-wise are very close to that in Figure 3, yet still yield notably different rotation point location results and might potentially be more technically proper in nature. This can be seen some in Figure 4. Again, I would be glad to address any questions or comments regarding what I did there. I am also not especially confident in my results partly due to concerns about the application utilized in the preliminary analysis of Figure 1. For example, I have observed that the scaling of vectors is a little off, which can actually throw results off quite a bit. And I do not know how inaccurate this might potentially be making any of my results.
So it is also possible that I am not even close to being correct with what I have tried to this point. And conceptually and in tangible terms, I please need someone to help guide me through what I have done thus far that might be correct and/or improper toward trying to obtain the needed solution as accurately as possible. Then I can hopefully move forward with other aspects of the project more confidently. Thank you very much. I really appreciate it.
Not being in a math classroom for some 50 years now, I am struggling to find the most proper solution for the following. It requires some math/geometry and/or perhaps physics knowledge that I have likely forgotten (or never learned to begin with).
Attached Figure 1 shows one example that needs to be adequately solved for. It is a preliminary analysis of upward movement of an object away from the ground, represented in vector form and as selected from video frames of the movement. At frame 170 (the green 170 circle and starting point), both vectors are one and the same. The movement then progresses through frame 185 (the green 185 circle and end of the desired analysis period).
Two notable movement types have taken place. One is a rotational aspect that creates a rotation point location (intersection) among the two vectors (the red 185 circle). The other is a generalized (translational?) aspect. In this case, the vector as a whole moves somewhat upward and to the right over the course of the period. Two items I do recall/retain are that if only the rotational aspect were present, then vector segment lengths from their top ends to the red 185 circle would be equal, and the top end of vector 185 would reside slightly below a line drawn perpendicular to the top end of vector 170.
It is the rotational component(s), and more specifically the rotation point location (intersection) among the two vectors, that essentially needs to be isolated as precisely as possible from the total vector movement(s). The rotation point location is critically used toward determining an effective weight of the object sensed over the course of the movement.
And in this case, because of the translational vector movement(s) also taking place, the calculated rotation point location (again the red 185 circle) is quite erroneous compared with where it actually is. Through vast experience, the actual rotation point location in this specific example is substantially lower than displayed. This is largely confirmed in Figure 2, which analyzes just the first few frames (170-172) of the same specimen. Luckily in this instance, it appears to indicate some very early rotation (red circles), before any notable translational movement begins that routinely and greatly influence calculated rotation point locations.
Now it is possible that I have come across a relatively simple yet effective solution at this point. Elements of that work can be seen in attached Figure 3. I would be glad to address any questions or comments regarding what I did there. Unfortunately, however, I am not especially confident in the results I have been getting, particularly when applying it to other test specimens. So I am not yet able to confidently move any further along with the project.
This is partly because more recently I determined an alternative solution or two that measurement-wise are very close to that in Figure 3, yet still yield notably different rotation point location results and might potentially be more technically proper in nature. This can be seen some in Figure 4. Again, I would be glad to address any questions or comments regarding what I did there. I am also not especially confident in my results partly due to concerns about the application utilized in the preliminary analysis of Figure 1. For example, I have observed that the scaling of vectors is a little off, which can actually throw results off quite a bit. And I do not know how inaccurate this might potentially be making any of my results.
So it is also possible that I am not even close to being correct with what I have tried to this point. And conceptually and in tangible terms, I please need someone to help guide me through what I have done thus far that might be correct and/or improper toward trying to obtain the needed solution as accurately as possible. Then I can hopefully move forward with other aspects of the project more confidently. Thank you very much. I really appreciate it.