Galileo and the Equations of Motion

The first of the three laws of motion formulated by Newton (1642-1726) says that every object in a state of uniform motion remains in that state unless an external force is applied. This is essentially a reformulation of Galileo's inertia concept. This is sometimes considered to be the start of modern science. Among many other well known things that Galileo (1564-1642) achieved as an astronomer, he also described the law of falling bodies that we know as s = ½at². The objective of this book is to analyze critically why these results are attributed to him and how Galileo came to these conclusion and how he formulated them. Such an historical study is not trivial. There are of course the texts that were published during Galileo's life, but even more important in this context are some of his unpublished early notes as well as the texts that Galileo, who was blind at the end of his life, dictated to Viviani who was taking care of him. Because of his trouble with the Church, these had to be hidden, even after Galileo's death. Later they were sold in parts and in so doing were dispersed and got nearly lost. Fortunately the Grand Duke of Tuscany, Ferdinando II, could recollected whatever he could find.

This book is a thorough historical study, mainly addressing the professional historian. To meet the objectives mentioned above, one has to know and understand first what was known before Galileo and second try to understand how Galileo was thinking and how he came to his ultimate conclusions. This is far from a trivial task. It is very difficult with our current understanding of physics and of our solar system to set our brain in a state of understanding that corresponds to the time and circumstances Galileo was living in.

Boccaletti is therefore zooming in and focussing on this specific task. Thus, this is not a biography of Galileo, and his adherence to the Copernican heliocentric solar system and his problems with the Catholic Church are not explicitly covered and only mentioned in as far as it fits the main focus: the equations of motion. More specifically he restricts the book to the study to dynamics and kinematics deliberately avoiding statics.

On the other hand, precisely the unpublished notes, known as the De Motu (written in the period 1589-1592) of the young Galileo and the Discourses (Discorsi e dimonstrazioni matematiche intorno a due nuove scienze) (written during 1635-1642) of the mature Galileo are crucial. The first was written during his first appointment in Pisa and discusses the Aristotelian-Archimedean dynamical principles of how bodies sink or float in fluids. The second was written during house arrest and dictated by the old Galileo. Both are important to explore and understand Galileo's mind. They were included in the complete works of Galileo that were only published some hundred years after his death. They were edited, studied, and commented by several people and the interpretation was not always the same. Other important sources are his Le Mecaniche which are lecture notes written during Galileo's teaching in Padua around 1592. A short version of these notes was published posthumously. When he was teaching on the same subject ca. 1598, this resulted in a longer version. Handwritten versions were circulating and rediscovered much later. Another text is the Dialogue (ca. 1630). This is, just as his Discourses written in the form of a dialogue between two characters, one of them being an alter ego of Galileo, and the other one is the one that is asking questions and that is instructed by the first. This form of writing was not unusual during Galileo's time.

Like in most historical studies there are many quotations, and they are often quite long. They can be either form Galileo's writing or from historians that have studied Galileo. In this book they are placed in the text and they form the backbone of the facts that are being told. To keep things readable though, they are not in the original language but are mostly given in an English translation.

There are, in accordance with the objective of the book, two parts: the period before Galileo, and the period of Galileo. The first part of course starts with the ancient Greek, in particular Aristotle, and continues with an overview of the Middle Ages and early Renaissance. Attention is paid to the first criticisms on Aristotle by a group at Merton College (Oxford) and another one, known as the Parisian school. Later the Italians joined the discussion in the sixteenth century in particular Tartaglia and Benedetti. Some historians have suggested that Galileo got his ideas directly from Benedetti, but Boccaletti argues that Galileo probably never read Benedetti.

The second part goes though the manuscripts of Galileo and shows how he gradually criticized the Aristotelian dogma's and developed his own ideas, mainly based on experiments. His favored experiment involved objects sliding or rolling down an inclined plane. The rumors that he would have dropped weights from Pisa's tower is most probably a legend. The inertia principle appears in several of his publications and letters. The dialogues in the Discourses go on for several days, so that they are subdivided into parts indicated as the first day, the second day, etc. Since these came to us in versions that were not published during Galileo's life, and editors later gave their own interpretation, it is not always clear what was really intended. Anyway, whatever relates to Galileo's study of motion of falling objects, or the inertia principle or the parabolic trajectories of projectiles and even some of his notes on the pendulum are brought to the foreground. Galileo also considered motion relative to different reference systems. At the end of the book, this is also briefly explained and why one can read in modern textbooks that the equations of motion remain invariant under 'Galileo transformations'.

Since it is not the focus of this work, it is not really stressed, but Galileo was also the one who started formalizing things and used mathematics and formulas, much more than what was usual in the Greek tradition. This is a book for historians, if you are interested in a biography or in his astronomical contributions or his dispute with the Catholic Church, one should try to find another book. For an easy reading biography I can recommend Galileo Galileo - When the world stood still by A. Næss (Springer Verlag, 2005).

Adhemar Bultheel
Book details

Newton's first law of motion is the law of inertia: every object in a state of uniform motion remains in that state unless an external force is applied. Other well known laws of motion are that the distance traveled by an object, traveling with a uniform accelerated speed, like a falling object is s = ½at², and the parabolic trajectory of a projectile. For all of these, Galileo has contributed to their origin. The purpose of this book is to explain how Galileo gradually transformed from a believer in the Archimedian approach to eventually arrive at the new insights of these laws of motion. Boccaletti carefully analyses the available texts to understand this transformation. This is a study mainly addressing the professional historian.



978-3-319-20133-7 (hbk)
105.99 €

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