# Combined motion (rectilinear-curvilinear)

2개월 전

Greetings to the entire academic and scientific community of steemit.

# Introduction

When we refer to movement we can say that we are talking about the phenomenon of greater impact on the activities of humanity, this includes both our body and the universe itself, because thanks to the action of this phenomenon is that any living species of this planet exists, including everything around us.

In the previous articles we were able to know the basic movements such as circular, parabolic, elliptical and hyperbolic, and to complement these fundamental mobilities we will relate to the rectilinear movement in order to begin to know the most complex or combined movements.

Any person is witness of the different types of movements that occur around us since they are immersed in nature, from there we have been able to study them and transmit them to the different activities of the human being through physical science essentially through kinematics and other complementary areas related to the study of movement.

It is important to express that according to the trajectory traversed by any particle, body or object we can determine the type of movement executed, that is to say, it is related to the geometric place of the figure traversed by these bodies, in this opportunity it corresponds to the essential straight line to offer its contributions in the analysis of so important phenomenon joining it with curvilinear figures such as the circumference and parabola, to generate the combined movements.

We already know the trajectories of the previous movements (circumference, parabola, ellipse and hyperbola) so it is important to start with the geometric description of the important straight line because it represents the trajectory of the phenomenon called rectilinear movement, and with which we go or constitute the rectilinear-curvilinear movement.

The straight line is undoubtedly the base figure for all those geometric bodies that surround us or shape our environment, which is why it represents the cornerstone for the development of any scientific area, and kinematics together with analytical geometry have taken advantage of these virtues to concretize and deepen the study of movement.

We can then affirm that if we want to understand any type of movement (either particular or combined) carried out by a given mobile at least in a general way it will always be necessary to be able to visualize the description of its trajectory, where the different geometric figures play an essential role.

# The straight line

With this essential geometric figure we have achieved the comprehension and development of innumerable activities carried out by the man, in the same way it has allowed us the understanding of different phenomena that surround us day after day during the development of our lives, where we find the recognized phenomenon of the rectilinear movement.

This figure is generally related to the definition of length when we refer to it as the shortest distance between two points, however, the straight line in terms of analytical geometry represents the geometric place occupied or formed by two different points such as P1(X1, Y1) and P2(X2,Y2) which belong to that geometric place.

# Rectilinear motion

Any one of us observes this type of mobility on a daily basis, so we can say that this particular movement is the foundation and cornerstone for understanding all types of mobility, even though the types of movements in our environment are generally curvilinear.

After analyzing the curvilinear movements, it is now up to the rectilinear movement to show its fundamental characteristics beyond its own comprehension and application, since it will join the curvilinear movements such as the circular and parabolic, forming combined trajectories.

In this way we will highlight one of the greatest qualities of both this type of rectilinear-curvilinear movement and the human intellect, as man through science has managed to combine different knowledge related to any mobility captured from our nature, some examples observed in the development of this article.

Therefore, according to the above expressed in relation to the straight line, we could say in a general way that a certain particle, body or object can move developing a rectilinear movement when in its trajectory or path it describes the geometric place of this straight line.

In our surroundings we find innumerable movements of rectilinear type, for example, when driving any type of vehicle we can transit by a rectilinear trajectory, a Pixer or pitcher in a game of baseball in a determined moment will use a throw called straight (without giving rotatory effect to the ball), where, the ball is thrown with great speed following the trajectory of the geometric place of a straight line, as we can observe in the following figure 1.

Innumerable examples could be found in our everyday life in relation to this rectilinear movement, however, its combination or relation with other types of movements makes it even more attractive and impressively useful for all of us as we will see later in the combined movements.

# Straight line and circular movement

This characteristic allows it to play a vital role in the study of the different movements of our environment, and without a doubt in those whose trajectories comprise a sector or some linear representation of at least intrinsic form.

In the circumference we find an essential element known as the radius (r), whose length is expressed geometrically by a straight line and in circular motion by means of the radius vector, and in this way we could achieve the location of any particle body or object that travels through the geometric space of a given circumference, carrying out the circular motion.

Although in the example mentioned, the straight line is not combined with the circular path, its use for the analysis of this movement is important since the position of the particle, body or object is an essential part for the study of movement in general.

A practical example which relates the straight line with a circular movement is represented by geostationary orbits, this type of orbit is recognized by the fact of keeping certain artificial satellites in synchrony with the earth by means of a circular movement, that is to say, that they turn in synchronized form with our planet.

In relation to the height required by this orbit we could say that it is the existing distance between any point of our planet with a point in space or geometric place of the circumference trajectory of this circular movement, which will represent the geostationary orbit, when joining these points we would obtain the figure of a straight line, as we can observe in the following figure 2.

As we can see in the previous figure 2, the straight line is immersed in innumerable analyses or studies of grandiose phenomena or activities related to our daily life, where movement has always been an essential part of our existence.

# Parabolic rectilinear motion

When we move in a car or any type of vehicle along a certain motorway or road, we can see that on certain occasions we come across straight paths and at the same time when leaving these we also come across paths, where we notice that we go up and down, that is to say, with elevations because these roads are built over some mountains and flat areas, in this way we have straight parabolic paths, as we can see in the following figure 3.

In the previous figure 3, we can observe a combined trajectory by a straight line and a parabola respectively, that is to say, a movement of parabolic rectilinear type, next we will show an example of this type of combination using again a pitcher or baseball pitcher as we can observe in the following figure 4.

# Rectilinear-parabolic-circular motion

This type of mobility is one of the most impressive combined phenomena since we find the connection of three different trajectories which are represented by the geometric place of the figures such as, straight line, parabola and circumference, originating also the nexus between the rectilinear, parabolic and circular movement, next we will observe the combined trajectory by these three geometric figures in the following figure 5.

This combination also represents a rectilinear-curvilinear movement but even more complex than the previous one (rectilinear-parabolic), this mobility could be observed in many cases when attending a amusement park through the so-called roller coasters, where we can find this magnificent combination of trajectories, and therefore of the aforementioned movements as we observe in the following figure 6.

The combination of particular movements has allowed us to enjoy even more the phenomenon of movement, since many of our activities require complex systems, devices or instruments that have combined mobility characteristics to carry out these activities no matter how complex they may be.

# Conclusion

Physical science throughout its history has made our world a home truly endowed with natural characteristics and transmitted to our daily activities, the understanding of the phenomenon of movement has been one of such characteristics brought by the scientific field to the rest of humanity.

By carefully observing all that surrounds us, both the natural aspect as well as the man-made one, we would see impressive movements either in a singular or plural way, and when we follow each route we can visualize each one of the trajectories travelled, therefore, we would draw with our imagination to such geometric forms.

The rectilinear movement in a general way represents the foundational and angular stone for the understanding of this phenomenon of global form, this movement makes use of the geometric place of a straight line in its route, and any person can observe a practical example of this mobility with only observing its environment since the same one is present in any instant of our lives.

Any type of movement of particular form is fascinating, and to be able to analyze it in detail will always be complex, this leads us to highlight how spectacular is a combined movement, whose main characteristic is then its intrinsic complexity, however, this linkage allows us to solve innumerable activities related to our development and therefore to our existence.

In this way we were able to enjoy the combination of the trajectories represented by the straight line, parabola and circumference, and with it the rectilinear-parabolic-circular movement, or from a general form of the rectilinear-curvilinear movement, and with this we generated the foundational bases for the next types of movements.

Until another opportunity my dear readers of steemit, especially the members of the communities friends of #steemstem and #curie for which I highly recommend to be part of these exemplary projects, as they highlight the valuable work of academia and the scientific field.

Note: All images were created using the Paint, Power Point and animated gif applications with the PhotoScape application.

# Bibliographic References

[1] Charles H. Lehmann. Analytic geometry.
[2] Lior M. Burko and Richard H. Price. Department of Physics, University of Utah, Salt Lake City.
[3] Snapper, E., Troyer, R.J. Metric Affine Geometry. Dover, New York, 1971.
[4] O. Montebruck, E. Gill. Satellite Orbits, Springer.
[5] Williams J. Astore, Robert B. Giffen, Wiley J. Larson, Understanding Space, second edition, 2004.
[6] J. Peraire. Dynamics - Rectilinear Motion, Fall 2004.
[7] Rectilinear Motion. Calculus-Based General Physics. University of Nebraska – Lincoln, 1975.
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